A capacitor is a small cylindrical battery-like part that stores and releases an electrical charge to start and run your AC's motors. A start capacitor delivers a brief, powerful jolt to get the compressor turning; a run capacitor stays engaged to keep the compressor and fan motors spinning smoothly. A failing capacitor is the most common air-conditioner repair there is.
Symptoms are easy to recognize: the outdoor unit hums but won't start, the fan won't spin, warm air blows while the system runs, or the breaker trips. Because outdoor units bake in the sun, heat is the number-one cause of capacitor breakdown; lightning and voltage surges also kill them. Most last 10 to 20 years.
Here is what matters for your wallet: the part itself costs only $8 to $50, and a complete replacement typically runs $80 to $400, around $175 on average — the cheapest of the common AC repairs. A dead capacitor produces many of the same symptoms as a far more expensive failed compressor. An honest tech tests the capacitor (and the contactor) first; be wary of a shop that jumps straight to 'your compressor is dead, you need a new system' when a $175 part may be the real fix.