Scrubbing is the action you do when searching through audio during postproduction. The name refers to the scrubbing a reel would do against a tape as it was searched using an analog system in the past. Of course, scrubbing nowadays is more often accomplished with digital editing software, where most programs will allow an editor to scrub through a sound file by positioning their cursor on its waveform.
Obviously not having to damage a physical tape is a big advantage of digital recording, but losing that sound effect is a hit to the charm. With digital audio, scrubbing gives the same jittery 'fast forward' effect that DVDs have -- so maybe it should be called jittering instead?
Hotkeys make the constant scrub-and-slice routine of sound editing more bearable. Especially when doing something tedious like ADR: hotkeys allow you to quickly tap play, listen or scrub through, tap delete or not, and rinse, repeat, retry. Saving ten seconds every time you check a take adds up when you have to get dozens of takes done before tomorrow.
You can scrub through video too, but audio is the first thing that comes to mind when I hear the term. You'd feel the same way if you spent weekends hotkeying through hours of actors saying the same lines over and over again.