Cut-off region: -
The transistor is off. There is no conduction between the collector and the emitter.(IB=0 therefore Ic=0)
Active region: -
The transistor is on. The collector current is proportional to and controlled by the base current (Ic=ßIB) and relatively insensitive to VCE. In this region the transistor can be an amplifier.
Saturation region: -