Aspects are one of the most interesting and important aspects of Fate. You can read about the rules here: http://fate-srd.com/fate-core/aspects-fate-points
Aspects are both similar to feats, in which you can use them for various bonuses, but are also a Rp tool, and a way of getting fate points. Aspects can be invoked or compelled, which means used to create an advantage or a disadvantage.
In addition to the characters, aspects can be applied to anything and anyone. Sometimes it will be obvious (“on fire”). Sometimes it will not be obvious (“hidden trap door”). Almost all NPCs will have hidden aspects (“Doesn’t like to be argued with”; “Cheats on his taxes”; “having an affair”). These can be learned in various ways, and then invoked to create an advantage.
You can create aspects by your actions (“spilled marbles on the floor”), and then invoke them for possible advantages. It works both ways, though.
When you create your aspects, you should have a little summary of what it means. “Toughest Elf In the World” could mean you’re hearty, or like to pick fights, or have no fear, or all three. You don’t need to wholly flesh it out, as flexibility is important, but we want to be on the same page.