What's the third wire on a piezo buzzer?
They're called self drive types, and they're meant to be used as part of the oscillator:  

  

The piezo effect works both ways: if you apply a voltage the piezo stretches, but also if it stretches it creates a voltage. This principle is used to create a feedback signal which drives the oscillator.
The advantage of the self drive is that it will automagically work at its resonance frequency, where it produces the loudest sound. In 2-wire circuits the oscillator's frequency is independent of the piezo's resonance frequency, and it's the designer who has to make that they're close.   

For the piezo of your picture:  


  "G" = black
  "M" = red
  "F" = blue  


(I guess M, F and G stand for Main, Feedback and Ground, resp. CMIIW)