Op Amp Understanding + Holiday Lights Tutorial
Per Jeremy Blum:


  If the input doesn’t have a audio input plugged in, then it’s said to be “floating” and you >can’t really count on the circuit to do what you would expect. The audio input connection >introduces a known voltage (0 when no sound is playing) connection between the positive op->amp input and GND that we then amplify. Try connecting the input to GND and you should see >the LED turn off.


Source: http://www.jeremyblum.com/2011/12/25/tutorial-14-for-arduino-holiday-lights-and-sounds/comment-page-2/#comment-1373392