You may remember the "Transistor as a Switch Circuit" which looked somewhat similar to this circuit. Howver, this circuit has two transistors. They are organised in such a way to amplify the base voltage.
The amplification (GAIN) in voltage by a transistor is called HFE. The gain of the transistors used here is 282 (BC337 transistors). The total gain is 282x282 which is 79,524.
This means the circuit is a lot more senstive and easier to tune.
You may also remember a schematic diagram similar to this one. It was named the "Capacitor as a Timing Circuit". The effect of the Darlington Pair in this circuit is that the capacitor charges quicker, but it also discharges faster as well.