That's strange, there are two different explanations of how the circuit works. And it's a simple circuit.
My theory is this:
The output of the op amp (someone called it a comparator) is switching between a GND and 9 V. Because those two voltages (0V and 9V) are on the supply terminals of the op amp. If there is 9 V on the output, there is no potential difference between the terminals and no current will run. If there is GND, there is a potential difference and the current will run, lightning up the LED. But there is something odd, why doesn't the LED burn out, because there is 9V? Maybe that 1K ohm resistors helps.
Well this is how I understand working of this circuit. Can someone with a lot of practice confirm it?
@Hero999 Sorry i don't have an oscilloscope, because i don't have the money for buying one. I have bought these electric components for $10.