The term bistable refers to a state of a circuit where the circuit with an external trigger is able to render itself stable (permanently) over two states: ON state and OFF state, hence the name bistable meaning stable on either ON/OFF states.
This ON/OFF stable toggling of the circuit alternately could be normally done through a mechanical push button or through a digital voltage trigger inputs.
Let's understand the proposed bistable transistor flip flop circuits with the help of the following two circuit examples:
In the first example we can see a simple cross coupled transistor circuit which looks quite similar to a monostable multivibrator configuration except the the base to positive resistors which are missing here intentionally.
Understanding the transistor bistable functioning is rather straightforward.
As soon as power is switched ON, depending upon the slight imbalance in the component values and the transistor characteristics, one of the transistor will switch ON completely rendering the other to switch OFF completely.
Suppose we consider the right hand side transistor to conduct first, it will get its biasing via the left hand side LED, 1k and the 22uF capacitor.
Once the right hand side transistor has switched completely, the left transistor will switch OFF completely since its base will now be held to ground via the 10k resistor across the right transistor collector/emitter.
The above position will be held solid and permanent as long as power to the circuit is sustained or until the push-to-ON switch is depressed.
When the the shown push button is pushed momentarily, the left 22uF capacitor now will be unable to show any response since its already fully charged, however the right 22uF being in a discharged state will get an opportunity to conduct freely and provide a harder biasing to the left transistor which will instantly switch ON reverting the situation in its favor, wherein the right hand side transistor will be forced to shut off.
The above position will be held intact until the press button is yet again pressed. The toggling can be flipped alternately from left to right transistor and vice versa by actuating the push switch momentarily.
The connected LEDs will light up alternately depending upon which transistor is rendered active due to the bistable actions.