| Vamp means to repeat a short one or two bar phrase "until ready." A vamp is played by the accompaniment until the soloist or instrumentalist is ready to begin. A vamp can last quite awhile in some circumstances.
An example would be when a singer is introducing a song to her audience, maybe telling some background about the song or who wrote it or why it is meaningful for the singer. Meanwhile, let's say, the pianist is playing a repeated vamp that sets the mood or tempo and possibly hints at what the song is. Or the vamp could be played by the bass and drums to set the tempo.
When the singer is ready to begin the actual song, she may nod at the musicians and then they start the song.
If you see the movie "Chicago" you will hear many vamps to music in the show. In that movie the background soundtrack vamps serve as a transition from spoken dialogue to a song and dance number. "Cell Block Tango" was a particularly well done vamp as the throbbing tango-like tempo begin very subtly, then built intensity until the song actually began.
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"Jazz sounds like a very good blues band that fell down a flight of stairs."
Michael Buble, Canadian standards singer | 
