In Burning wheel gold character traits have little mechanical effect - they may give an artha reward in some situations.
The obvious effect of character traits is to inspire and remind players to play according to the trait. They might also inspire GM to present a situation where the trait might cause trouble or interesting choices for players.
Is there more? How have character traits significantly affected your play? As a game master, how should I advise players to think about character traits in order to have them select or come up with suitable ones in character burning?