Aspects are elements of Gamedec's characterization that cover many different sides of a character – some of them are typical traits, some 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, depending on the Values chosen for player character. 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.
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.