I think breakdown originally came from referring to the drum break of a song. It may help to "break" up the monotony of an arrangement, so that when the same chorus/riff/whatever kicks back in, it sounds a bit fresher (pop songs often employ key changes at this point too). It could also be a transition to a new section of a song, so it all depends on the particular tune you're talking about. Overall though, I think it's a device used to create interest for the listener (and possibly give the other musicians a rest!)