Hi Bunch, "book" is a casual synonym for schedule and "gig" in this context means a performance, so "book a gig" here means "schedule a performance". B can't quite answer A's question of where they play because he hasn't scheduled any public performances yet. Hope that helps.

the word 'book' here is functioning as a verb meaning to arrange (book: to arrange to have a seat, room, performer, etc. at a particular time in the future) the sentence would have the same meaning like this: Uh, well, I haven't exactly arranged a gig yet. In the context of the sentence 'gig here means performance (gig: a single performance by a musician or group of musicians, especially playing modern or pop music).

Hi Bunch, a "gig" is a musical performance. It's normally used when the musical performance is that of a band or a singer who are playing certain genres of music e.g. rock, pop, jazz. It wouldn't be used for a classical performance, for that you'd still call it a classical performance. I hope that helps. :)