I always assumed he was hyperventilating to get as much oxygen as possible in his blood before the jump. He would have to let the air out of his lungs before jumping but I never felt like anything in the scene contradicted that.
The interesting thing is that Arthur C. Clarke was a very experienced scuba diver and still had a problem with the scene. Ah well.
It's one of my favorite action scenes in any science fiction film. The interesting thing is that the trick just relied on good photography, piano wire and dropping Keir Dullea. It's easy to imagine how a present-day director would mess that scene up with CGI effects, slow-motion, stuntmen, and so on.