Output frequency of bistable multivibrators
You can find an explanation of how the circuit works on Electronics Tutorials.

When a low signal is sent on the trigger line, the pulse is transfered through the capacitors. Whichever side is high (anode of D1 or D2) is pulled low, causing the transistor on that side to turn off. The next trigger pulse reverses which transistor is on.

The reason that the output is half of the input is that it takes 2 trigger pulses to have one pulse on the output.