There are also some more specific senses than just to finish or complete something. Often it means to summarize a talk or discussion. It can be used like this as a verb: " This discussion has been very interesting, but could you wrap it up." is asking to summarize and end. Or it can be a noun " After this break, we will have the wrap up of today's show"

it means to finish as in a process or a conversation.

It means to end the performance or the show.