To understand this, think of your kitchen sponge. Put it under the tap, and it soaks up water. Now squeeze it. The water comes out. It was in all those tiny, porous spaces inside the sponge.
Compression is like that.
And the 0's. Lots of them, too. That means faster transmission times, faster downloads. It removes extra information, the redundant and irrelevant parts of a sound signal that the human ear doesn't hear anyway. It shrinks the original sound data from a CD by a factor of 12 without sacrificing sound quality.