Although audio tapes and video tapes look different, they're based on the same principles. Each has a roll of magnetic material which slides past the so-called "playback head" in the VCR or cassette deck (cassette decks have one playback head, VCRs have two or more).
In both machines, these heads detect changes in magnetism as the tape moves by. The changing magnetic signal is translated into music on your tape deck, or both video and sound on your VCR. Without a changing magnetic signal over a playback head, you'd get no sound, no picture.
But here's a mystery: When you press pause on the VCR, the screen doesn't go blank. Instead, you get a frozen image. Remember, you need a changing magnetic signal to create even a still video image. If the video tape isn't moving, where is this changing signal coming from?
We're used to VCRs doing this, but it's actually kind of strange. It would be like pressing pause on a cassette deck and having the sound remain in your speakers, Pavarotti holding his high C until you press play again. VCRs do this trick by moving both the tape, AND the playback heads, which spin rapidly past the tape as it moves through the machine.
Pausing a video tape does indeed stop the tape, but it doesn't stop the spinning playback heads. These continue to swipe past the stationary tape, detecting enough of a magnetic signal for one still frame of video. Modern, hi-fi VCRs automatically mute the sound when they are paused, so you don't get a sustained audio sound as well!