Companions are individuals with talents that will help you in your quest. Most will stay with your party but there's a few specialized ones known as Independents that you can have travel off to perform tasks for you, like buy something from a merchant or harass a rival.
Some companions will be found for hire at the guild. Other may be found as a random event. In that case, a player may be able to convince them to join their party depending on their social ratings. If not, they can still hire them, unless they're animals. Players may be able to steal them from their rivals, as well.