Capacitors have several uses in AC circuits. To a DC circuit, a capacitor looks like an "open circuit" that can store a and source a charge. In an AC circuit, a capacitor reduces in impedance (resistance) as the frequency of the AC increases.

So the ways a capacitor can be used in AC circuit are:

1. DC energy storage - usually using a diode to "rectify" the AC into DC. Usually used for power supplies.
2. DC blocking - allowing high frequency AC to pass while appearing "open" to DC. This is very common in audio amplification.
3. Create a resonance - when an inductor (coil) is added to the circuit. These are most commonly AC frequency filters.

The capacitor in the microwave could be any of these 3 but given the high maximum voltage, it's likely number 1. Non-polarized capacitors can have a much, much higher maximum voltage than polarized ones.