The air conditioner contactor is a switch located in the outdoor part of the air conditioning unit. The “switch” consists of a control coil, a metal plunger, and one or more sets of electrical contacts. the switch turns the unit on and off when energized by the thermostat settings indoors.
This is a minor repair and can usually be diagnosed quickly. It is nort recomended for the average homeowner to attempt this procedure. There is a danger of high voltage and wiring wrong could produce many other problems.
Below find a youtube video with a very good explanation of the problems that you might have with a HVAC contactor.
Contactors vary from $12.00 to $50.00