Aspects are elements of Gamedec's characterization that cover many different sides of a character – some of them are typical traits, some describe assets in possession of your character, Aspects can also tell you about Gamedec's background or skills. Think of them as tags, if you like. Few of them we gain during character creation. After answering a set of questions, you are presented with a bunch of Aspects that seem to define your character best. You will gain most of them during your playthrough. Choosing a vicious answer during dialogue, or showing MacGyverish level of problem solutions will give you certain Aspects.
Beware, because you may also lose an Aspect. For example: if you have the "Rich" Aspect, people from higher reaches of society will be more willing to talk with you. If you spend too much money, you will lose the "Rich" tag, and dialogue options available before will be greyed out. Aspects, while describing your character further, are here for a different reason. They are used as a currency for unlocking different branches of the Profession tree. And Professions are – next to the Deduction system – your primary way of leading your investigations.
Think of them as skills you obtain to unlock specific dialogue options or environmental actions. Want to manipulate your suspect? Professions are your answer – unlock a profession to be master in people skills. Locked door? Bypass the lock if you chose to go with a "Hacker" profession.