AC capacitors will work with any polarity, whilst DC capacitors will only work with one polarity. An AC capacitor can work in a DC application, but a DC capacitor won't work in an AC application(where the polarity of the charge on the capacitor can flip). One might ask "why use DC capacitors at all?". And the answer would be that AC capacitors are usually significantly larger and more expensive for the same voltage and capacitance rating than DC capacitors.
Capacitors perform a variety of functions in circuits such as energy storage for short term demands in power supplies, signal coupling in AC circuits, tuning for frequency generators, power factor correction in AC power systems, stability control in amplifiers, and in filters.