The bistable has two stable states. At switch on, one transistor is ON and the other is OFF.
This is one stable state.
An external pulse makes the circuit change state, with the ON transistor now OFF, and the OFF transistor now ON.
This is the second stable state.
Since the two transistors are not exactly the same, one , say Tr1, will start conducting before the other, Tr2. As the current through Tr1 increases, the voltage across R1 increases and the collector voltage of Tr1 falls. This fall is coupled to the base of Tr2 via R2, causing the collector current of Tr2 to fall and its collector voltage to rise. This rise in voltage is cross coupled to the base of Tr1 increasing its forward bias and increasing the rise of collector current.
Since the collector current is already rising, the effect is CUMULATIVE and the collector voltage of Tr1 falls rapidly and the collector voltage of Tr1 rises just as quickly.
The circuit is now in one of its stable states with the collector voltage of Tr1 low, and that of Tr2 high. D1 has a low voltage on its cathode via R5 and a high voltage on its anode via R3, making it forward biased. D2 has a high voltage on its cathode via R6 and a low voltage on its anode via R2, making it reverse biased.
An external negative pulse is steered to the base of Tr1 since D1 is forward biased, but blocked from the base of Tr2 by reverse biased D2. Tr1 is turned off and Tr2 is turned off by the cross coupling. This happens very quickly because of the cumulative effect mentioned earlier. The circuit is now in its second stable state and waits for another trigger pulse.
Since the collector voltage of Tr2 changes state for every trigger pulse, there is one pulse appearing at its collector for every two pulses in.
It can therefore be used as a divide by two circuit.