Quadrants

The word 'quadrant' comes up, as in 2 quadrant controller or 4 quadrant controller. The word 'quadrant' comes from a graph. The graph below shows the blank on which you might start to draw motor voltage and motor current.

At the top right, both motor voltage and current are positive: the motor is driving in the forward direction. To brake the motor, the current must be reversed but the voltage remains positive as the motor is still rotating in the same direction. so forward braking is the top left quadrant.
The bottom two quadrants are for reversing.
So a '1 quadrant' drive gives forward drive but no regen braking and no reversing. A 2 quadrant gives forward drive and braking bit np reversing - yes one which gave drive but no braking , with reversing, would also be 2 quadrant, but this is not usually used.
A 4 quadrant drive gives reversing with regenerative braking, thus operating in all 4 quadrants.