I’m going to add a little Daniel answer.
FATE is centered around a mechanic called “aspects”. An aspect is a sentence that describes something about a character, a place,… For example, the Archduke of Boeruine could have an aspect like:
“I will do anything for the Iron Throne”
When playing, if your aspect is related to a situation a lot of things can happen. If it’s related in a good way, you can spend a FATE point (invoke an aspect) to do things like:
- re-roll, add a big bonus, make a narrative declaration that becomes true in the world,…
If bad (compel an aspect):
- bad things happen to you, but you get a FATE point.
For example, if Boeruine was dueling Avan and he missed a strike, he could declare that the aspect applies because losing that duel would lower his chances for the Iron Throne. So he spends a FATE Point and gets a re-roll.
But for example in an argument in the Senate, while trying to defend something, the GM can tell Boeruine that because everyone knows his ultimate goal is the Iron Throne, people are wary of his proposals. If the player accepts the complication, then the NPCs are wary of him, but he gets a FATE point for the trouble.
The nice thing of aspects is that they can be anything. The College of Sorcery is rumored to be “a place of secret knowledge”, the Gorgon is “the oldest enemy of Anuire”, Ilien has developed into “a thriving city for merchants”, and a weapon can “lust for the blood of scions”.
About the centered rolls, that’s not always the case. While most games use 4dF (which is the same probability curve as (d3-2) + (d3-2) + (d3-2) + (d3-2)), other games (like Legends of Anglerre, a fantasy version of FATE) uses d6 - d6, which has a more “random” curve.
The difference between both is the economy of FATE points, in LoA they are spent and earned faster and characters have more of them on average (to compensate for the more random rolls). But you can play LoA with 4dF if you prefer giving more importance to skills (skills are added to dice rolls).
Appart form that, another good link to read about FATE is:
http://stuffershack.com/xtras/playing-with-fate-learn-how-to-play/
3 short articles that make a nice intro to the system. Hope it helps!