If a controller started the compressor the moment the cabinet rose a fraction above setpoint and stopped it the moment it fell back, the compressor would switch on and off every few seconds. That is very hard on motors and contacts. The differential, or hysteresis, adds a band: for example, stop at 3 °C and restart at 5 °C.
A narrow differential holds a tighter temperature but makes the compressor cycle more often. A wide differential reduces starts but lets temperature swing further. Manufacturers choose a sensible value for the application; pharmacy and vaccine units generally use tighter control than a back-store drinks chiller.
Many controllers also have a minimum off time, a delay before the compressor can restart. This protects the compressor after a stop or a brief power interruption, giving pressures time to equalise. It is why a unit sometimes waits a few minutes before restarting after a power cut, which is normal and not a fault.