Entertainer mission terminals provide players with gig missions. Upon the accomplishment of a mission the player receives some credits and bonus experience as a reward.
In the mission listing will be various cities on the planet with a cantina or theater. When you take a mission, you must enter the specified establishment and either dance or play for the required amount of time. At the end of this period, you will get your reward. The type of dance or music has no effect on the mission, nor does the type or amount of flourishes used.
This gives Entertainers a small source of income for doing what they would already be doing--dancing or playing music.