Aspects are a game mechanic defined by the FATE system. You can read all about them on the online SRD by Evil Hat. It’s a pretty good resource. I recommend it.
The way I like to explain Aspects is this. Imagine that you took a regular yellow highlighter and marked up all the interesting keywords and phrases that are floating around in the air when describing what our characters are doing. Those are Aspects. They are the parts of the narrative that we are drawn to because they are the most interesting. All you have to do to interact with Aspects in the game world is simply have your character interact with the fiction. If you want to use an Aspect to give your character a boost, describe your action so that we understand how the Aspect has come into play in the context of the scene, and you’re good. You can take either a flat +2 to your roll or if that isn’t gonna cut it you can re-roll entirely.
The GM will create a lot of situational Aspects because the GM crafts a lot of the scene, the background, and what not. The players all define the Aspects on their characters, but they also add to the situational Aspects by using the create advantage action. Use this action. It is your friend. It literally enables you to shape a scene. Here’s how it works. You start with the scene as described by the GM, then your character takes action and changes it, thus creating a new Aspect in the scene. Awesome right? I know, I know.
Anyway, read the SRD if you want all the crunchy details. It’s pretty straight forward.