Im sure that Rick and Spaw and probably others understand how the piezo wafer works but for the sake if others I'll try to explain with being "sciency". For simplicity sake a piezo wafer that is found in a Radio Shack buzzer is a very thin piece of crystal sandwiched between to conductive plates.

When a crystal is flexed, even microscopically, it gives of a small electrical charge. The vibration that causes the flexing can be as single tap or a vibrating top on a guitar. The piezo pick up takes these electrical pulses and sends them down the wire to the tuner and it reads them as tones. Fewer vibrations equall low tones more equall high tones. Because the crystal creates its own electricity no outboard power is needed to make the sound travel down the wire. The batteries in the tuner allow the tuner to read and amplify the signal into a useable form for the tuner to work.

Magenetic pick ups are a powered pick up that reads a signal vibrating in a magnetic field. The principle of slow and fast vibrations is the same however.

Thats a very basic explanation. There are engineers who can explain it using better science but thats it in a nutshell.

Don