It comes from tape deck days.
With smaller track counts....like a machine that only had 4 tape tracks...you could record on 3 of the tracks and then mixdown and "bounce" them to the 4th track, freeing up the other 3 tracks for more recording.
Now days with digital audio, the term "bouncing" gets used for a few things...like submixing many tracks to an aux track for processing or for creating as stems for simlified mixing, or it might mean the creating of a new audio track with FX/Processing when you can't run a lot of plugs in real-time....and I'm sure there are a few other meaning that people in the digital world have applied to the term....but it comes from tape days.