WHAT IS "ROLEPLAYING"?
In its rawest form, roleplaying was a bunch of kids running around pretending to be something they were not. They might have stuck to a general theme or setting, such as "Cowboys and Indians". These games had a tendency to break down when one player's goals conflicted with another's. Somebody yelled, "Bang! you're dead." and somebody else yelled, "No I'm not!". In the 1970's, a kind of breakthrough was made by adding dice mechanics from strategic simulations ("wargaming" such as "Napoleonics") to improvisational theatre (the "mime" fad). Thus was born the Dungeons and Dragons craze.
There are several arenas for RPing today. There's the traditional tabletop gaming, a.k.a. "pencils and dice" or "paper" gaming. Generally there are three to seven Players and one Gamemaster (GM). The events in the game take place over a series of sessions, a "campaign" (a word borrowed from wargaming). Each player generally controls one character, with its physical, mental, social abilities, plus any unusual powers and weaknesses recorded on their "character sheet". The GM is the referee, playing the parts of all the characters that the player's characters (PCs) meet. These non-player characters (NPCs) can be friends or enemies. The GM is also in charge of explaining the environment and situations to the players, allowing them some freedom to choose their actions.
From this has grown live-action gaming (which has much more streamlined rules for conventions and parties) using either padded weapons or non-contact resolution mechanics like rock-paper-scissors. Another major arena is online gaming, which varies wildly but in some communities has progressed to having almost no interference by a gamemaster. In online gaming, the game is always running-- 24 hours a day, 7 days a week-- which earns it the name "persistent" gaming. NPC's are assumed to be present if it is appropriate to the setting but are not played by a GM.
It's important to point out that plenty of gamers feel the "acting" side of RPG is optional. Lots of people have fun with the mechanical side of it, with simple goals like "Kill the monsters, take their treasure." RPGs usually have a mechanic by which play is rewarded, usually "experience points" which can be traded in to upgrade the character's abilities or get rid of their handicaps.
After playing a character for a time, their character development and the relationships they have formed is what makes their player value them, not just their high "stats". Some people feel "put on the spot" by having to think fast, and speak in-character in the "first person". Others consider the persona side of it "true" gaming, the highest goal to which they aspire.
Thus, roleplaying is about being in-persona and talking to other players' characters. At its best, it is also about participating in a shared reality (the "Continuity"). The goal is not to "win", the goal is to participate in an ongoing story that's meaningful and makes sense to all the players.

FATE LEVELS

A common problem with gaming is dissatisfaction with the direction of the campaign. Games often fall apart when players learn that the game was not what they expected. For a long time it was assumed that this was normal and that the only way to find out if you would like a game (or gamemaster) was to try it and see. If a player had a poor experience, they were likely to assume that roleplaying in general was not for them, or that this particular gamemaster was a "bad" GM. The Fate System gives a perspective that there are many aspects to roleplaying, and that there are many places where compromises can be made. It also gives GM's insights into what players want, that they might not have already realized.

WHAT ARE FATE LEVELS?

There's as many ways to play an RPG as there are individuals. Each player naturally tends to form their own philosophy, usually without thinking much about it. The Fate Level system describes what appear to be five independent philosophies. Each is described in terms of criteria or parameters which could be chosen independently. However, they're all inter-related, and choices made about one aspect tend to force choices about other areas. They are not the only five ways to play, but they're definitely the five strongest and the five most common, because they are consistent and produce a recognizable and stable "flavor" of game.

THE CRITERIA SCALES

Here are the ingredients that can go into formulating a philosophy of play. The ones listed are the ones that players tend to intuitively assume go hand-in-hand with others of the same level (for instance, they are likely to assume a dark tone if the mechanics are complex and there's alot of adult content.) Unusual combinations will succeed best if players are made aware of those quirks in advance.

1. Player Control vs. Randomness --Dice or no dice, Character sheets, no character sheets?
2. Silliness vs. Seriousness --Light or dark tone?
3. Player Imagination vs. the Authors of the Game World --How much "study" is required to play?
4. OOC (Out Of Character) Fairness vs. Organic IC Consequences
5. Family Fare vs. Adult Content
6. Temporary Improvised Incidents vs. Permanent Continuity --How much "intrigue" is possible? Are characters related by blood, or maybe marriage? Are there established organizations already in this world?
(There are others, but these are the most important.)

The dominant or central scale is importance of "Continuity." Continuity includes your theme, your setting, your history, and how much previous events shape future events. ("Dungeon crawl" medieval fantasy might have a well-formed setting but the episodes don't happen to be interrelated like a serial.) It's good to have the other choices be harmonious because most players tend to assume that the other parameters are going to be similar. This is why Fate is divided into "Levels": because people tend to see them that way, and because they do form a natural kind of spectrum.

DESCRIPTIONS OF FATE LEVELS

Fate 1: Fantasies

"My character is my property."
Description: At this, the lightest level of Fate, the player is almost a GM. Players have maximal control over their characters and their characters' destiny. When Fate 1 characters interact with other characters online, the course of their conflicts are privately pre-negotiated. The game is more like interactive storytelling. At Fate 1, players are still expected to support IC continuity, i.e., there are limits to how farfetched the outcomes can be, and they must still stick to the rules' definition of their character.
        Can use dice: NO
        Can wound/be wounded: ONLY VOLUNTARILY
        Can kill/be killed: NO
        Can remove others/be removed from game: NO
        Can engineer deaths/removals from game: NO
        Can request OOC data related to their character: YES
  
Notes:
* This is still, with minor modifications, the most common philosophy of online gaming, and the least common tabletop. It requires no special coding, can even be done on IRC or via email. * "Does this mean Fate 1 characters are necessarily non-violent?" No. It only means the combat is diceless, and deathless.

Fate 2: Lighthearted

"I want control of my character but I don't want a cakewalk."
Description: The rolls of dice indicate whether or not their character succeeds in any particular endeavor where system is relevant. Characters can take and deal wounds, but all lethal wounds bring their targets to incapacitation, and not beyond.
        Can use dice: YES
        Can wound/be wounded: YES
        Can kill/be killed: NO
        Can remove others/be removed from game: NO
        Can engineer deaths/removals from game: NO
        Can request OOC data related to their character: YES
  
Notes:
* At this Level, a player might ask the GM a question like, "Is it dangerous for my character to be in this part of town at night?" Limiting the player to in-character knowledge is more relaxed because the game is less "serious".
* "What if I hurt someone pretty badly and they later die of blood loss or complications?" Simply put, they are not -allowed- to die as a consequence of your actions. This is a form of destiny control that you're exerting over their character due to your Fate rating.

Fate 3: Serious

"In Character Actions Yield Fair In Character Consequences."
"I am a part of the Continuity; I share control of my character with the game world and the game."
Characters can roll dice, and take levels of damage. Characters can be removed or remove other characters from play, can engineer that removal or death, can kill and be killed.
        Can use dice: YES
        Can wound/be wounded: YES
        Can kill/be killed: YES, IF IT IS MEANINGFUL TO THE STORYLINE.
        Can remove others/be removed from game: YES
        Can engineer deaths/removals from game: YES
        Can request OOC data related to their character: NO
  
Notes:
"Meaningless Death" Clauses
In a GM'd game, the GM may fudge a dice result that gives an outcome that was not a justifiable consequence of their in-character actions.
In an online situation: If the present conflict did not arise out of a conflict in which your character killed another, you may, before the conflict, opt for a no-death outcome.

Fate 4: Mature, Potentially "R" Rated

"In-Character Actions Yield In-Character Consequences, but there may be some things I will not roleplay." Players now have the option to be fully immersed in their characters; OOC interaction and knowledge is minimized. Players are considered to auto-consent to death.
        Use dice: YES
        Can wound/be wounded: YES
        Can kill/be killed: YES
        Can remove others/be removed from game: YES
        Can engineer deaths/removals from game: YES
        Can request OOC data related to their character: NO
  
Notes:
* In most tabletop games, this was the original default. Refusing consent for a character to be injured, killed, etc., was unheard-of. It's still the default for Ultima Online and other games with coded combat.
* "But what if I'm sitting in a bar, a crazy walks in, pulls out a submachine gun, wins initiative, deals me twelve levels of damage, and that's that?" The short answer: Your character dies. (Perhaps you shouldn't have been sitting in a bar, or you shouldn't have chosen Fate 4.)
* Overall coherence of story tends to suffers at Fates 4 and 5, because there is no pressure for deadly conflicts to have a reasonable IC explanation.
* The Continuity of an online game suffers at Fates 4 & 5, as characters die more often.
* Online: Consent is not assumed for "darker" fates, some of which can be brought about by the use of unusual powers such as mind-control, and shapeshifting of others. In some places, storylines involving maiming, torture, rape, and other adult themes, require one to be Fate 5, and Fate 5 requires being a legal adult.

Fate 5: Potentially X-rated

"No holds barred."
"Reality bites, and so do I."
        Use dice: YES
        Can wound/be wounded: YES
        Can kill/be killed: YES
        Can remove others/be removed from game: YES
        Can engineer deaths/removals from game: YES
        Can request OOC data related to their character: NO
  
Notes:
* This Level involves what is called "Black Dog RP": roleplay of a decidedly adult character which may involve rape, torture, graphic sexual or violent scenes, pedophilia and so forth. Players automatically consent to absolutely anything befalling their characters.

HOW DO WE APPLY THEM?

There's several ways to use Fate Levels. Each has its advantages and disadvantages.

METHOD 1: By Individual Choice

Here is the way its creator originally envisioned the Fate System being applied: Each player voluntarily tags their character one Fate. They may not take actions that would force consequences beyond their Fate Level. Conflicts between varying levels are solved at the lowest level present. Fate may be "darkened" (raised) at any time by the player, but lightening (lowering) is only done in very special cases, by the GM. (Alternately, I suggested lightening might be done voluntarily but with a heavy cost in experience points.)

   ADVANTAGES: Everybody is happy with the freedom provided.
          Players whose Fate Level is not well-represented at
          the moment can still participate.
   DISADVANTAGES: The overall game tends to be dragged to the
          lowest common denominators, i.e., Fate 1-2.  Areas
          with mostly Fate 5's suffer serious continuity damage
          due to IC fatalities.

METHOD 2: By Region

Especially for Online games, this is simply a ban on action of lower Fate Levels in certain areas. In this version, players don't bother tagging themselves.

   ADVANTAGES: Less hassle for players; conflicts are solved in a
         more predictable way.
   DISADVANTAGES: No telling what other players' favorite play style is.

METHOD 3: By Game

The whole game is limited to one play philosophy, and everyone is expected to follow it.

   ADVANTAGES:  Permits a "custom" formula for the game.  For example,
        defining it as Fate 5 but only permitting X-rated violence and
        not sex in public places.
   DISADVANTAGES:  There may not be enough people who happen to want
        to play the way envisioned.

A NOTE ON THE FATE SYSTEM

First devised and copyright 1995 by Jon Peterson for online roleplaying, the Fate Level concept has much application in face-to-face gaming as well. Online, it represented an advance in gaming vaguely analogous to the changeover from an arbitrary monarchy to constitutional democracy; when applied back to traditional tabletop gaming with a GM (gamemaster), it resembles a change to a constititional monarchy.

The Fate System encourages longterm fun by getting the players and GM to understand, and state, in advance, what it is they hope for. The game is no longer forcing game outcomes on players, it's giving them that to which they've already agreed. After three years of testing, it has emerged as the most successful method by which to run a persistent online game in the all-text (MUSH/MUCK/etc.) community.