This is a Constant Current Source LED Driver, When the LED driver Upper-NPN is driven by a voltage thru 4.7K the LED lights up. Assume that the Lower-NPN at bottom is absent. The current via LED and NPN is limited by R. 20mA may be ok 15mA even better. Or LED blows even transistor goes.
BC547 is like 100mA-40V-200b, Limit collector current to 60mA, use it at less than 25V and depending on the individual transistor you may get a DC current amplification of 200 times. That is 1uA of base-emitter current could give a whooping 200uA of collector-emitter current.
Still Thinking we do not have the Lower-NPN we calculate the resistor. Vcc - ( 2 LEDs * 1.7) - Vce = Vr that is the voltage across the resistor. You know ohms law and the current needs to be 15mA for a bright and long lasting LED. Lastly 1.7 the forward drop of a green LED and 0.6 a saturated or Turrned-On NPN Vce.
Now you use the Lower-NPN, The above calculations do not hold anymore. Let us think a small current is flowing in the LED. Then the voltage across R is less than 0.7V, that means base-emitter diode of the Lower-NPN will not get to conduct. The Collector does not draw any current away. Now think that more current flows in LED, the voltage across R builds up above 0.7V the Lower-NPN is biased. The collector of Lower-NPN starts drinking current from the base of the Upper-NPN. So The Upper-NPN starts losing its bias. This lowers the LED current and contains, regulates or controls the LED current as shown in the formula.