central a/c won't cool
It could be a variety of things, but there's no way to be sure without troubleshooting the system.
Thermostat
It could be that the thermostat isn't signalling the A/C unit to start.
Things to check

The indoor blower comes on
The outdoor unit turns on
There's voltage on the A/C signal wire from the thermostat


Control board
The control board in the air handler/furnace could be bad.
Things to check

The indoor blower comes on
The outdoor unit turns on
There's voltage on the A/C signal wire to the A/C unit


Contactor
If the contactor is bad, the A/C unit will get the signal to come on, but the unit will not turn on.
Things to check

The outdoor unit turns on
There's voltage at the normally open contacts of the contactor (T1, T2, T3)


Blower
If the blower in the air handler/furnace is bad, cool air will not be blown throughout the home.
Things to check

The blower in the air handler/furnace comes on
Air flows from the supply ducts


Condenser fan
If the condenser fan isn't working, the system will have difficulty removing heat from the refrigerant.
Things to check

The fan on the outdoor unit (condenser fan) comes on


Compressor
If the compressor in the condensing unit is bad, the system will not move refrigerant through the system.
Things to check

The refrigerant lines are different temperatures
The compressor turns on (may have to touch the unit to tell)


Restricted air
If air isn't moving through the system properly, it won't work well.
Things to check

Air is being moved by condenser fan
Condensing unit coils look clean and free of debris
Air handler/furnace filter(s) are clean
Air is flowing from the supply ducts
Evaporator coils are clean and free of dust and ice


Refrigerant level
If there's not the correct amount of refrigerant in the system, it will not function properly.
Things to check

Refrigerant lines are at the proper operating temperature (requires knowing the operating temperature)
Operating pressure of the refrigerant lines (requires a set of gauges)