4-quandrant:
A machine or motor-drive+machine can operate in different modes, the number of quandrants give a very good indication
The for quadrants are:
Forward motoring
Forward braking/regen
REverse motoring
Reverse braking/regen
The quandrant part comes from the fact this is usually plotted on an X-Y graph with Speed on the X-axis and Torque on the Y-axis
An induction machine hooked to the utility is known as a 1quadrant since it only motors in one direction.