When you look really closely at record grooves, like at 1000x magnification, you can see the waveforms of the music itself. Sooo cool.
This video shows how the stylus moves through the grooves.
As Lisa Simpson would say, "I can see the music!"
Update: Here's a great visual explanation of how you get stereo sound out of a record. (via @pcnofelt & @marcrobichaud)
Update: This is a much better video showing the needle riding through a record's grooves.