A gig was an artistic performance or task one was hired to do, such as a concert.
In 2375, Vic Fontaine disappointed Rom after the Ferengi's less-than-stellar rendition of The Lady is a Tramp, saying he didn't get the gig. (DS9: "The Siege of AR-558")
Later that year, Nog asked Fontaine to cancel his upcoming gig, as he still wanted to "hang in" (hang out). Fontaine explained that he couldn't, because it was unprofessional, and performing was his life. (DS9: "It's Only a Paper Moon")
In 3190, Michael Burnham recalled doing "borderline-legal courier gigs" with Cleveland Booker. (DIS: "The Examples")