I was told by repairman that my compressor to my a/c unit had quit working and that it was time to replace the whole unit. Just for my understanding can someone tell me what could have caused this to happen.

Any of a dozen different things

No power
Old/worn out
Low on refrigerant
Bad contactor
No low voltage (24 volts )kicking in the contactor
No power to the furnace/contactor
Broken wire either low voltage or high voltage
Probably could come up with a couple more,
But would need more info than what you sent us