A contactor is the electrically operated switch in your outdoor unit that connects high-voltage power to the compressor and condenser fan. When the thermostat calls for cooling, a low-voltage signal energizes the contactor's coil, which pulls a set of contacts together and sends 240 volts to the equipment. When the call ends, the contacts open and the unit shuts off.
Because those contacts make and break high current thousands of times a season, they wear: the surfaces pit and burn, and the contactor can stick closed (the unit never shuts off) or fail to pull in (the unit hums or does nothing). Ants and other insects are a surprisingly common culprit, crawling in and getting crushed across the contacts.
The contactor is a cheap, fast fix — typically $100 to $350 installed and well under an hour of work — but its symptoms overlap almost exactly with a failed capacitor and even a failed compressor. That overlap is where overselling happens. A competent tech checks the inexpensive electrical parts — capacitor and contactor — before condemning the compressor or the whole system. If you are told you need a new unit, ask whether the contactor and capacitor were tested first.