In Star Wars The Old Republic companions are vital in your missions as they aid you 100% of the time, specially if your are playing solo.
Vette is one of the companion for Sith Warrior, as you gain affection points by conversations or by giving her gifts there will be a mission that will be unlocked, this applies to other companions as well in other classes.
Mission Star of Ryloth is about retriving a Twi’lek artifact. during your conversation with Vette she will tell you that she received a message from on of her old gang.
You are to aid her in retrieving the artifact, with success you will meet her old gang. This mission will earn you affection points if played right.
Also remember that romance is available in Star Wars The Old Republic, to do so, you will need to earn more affections points.