The diaphragm of a condenser microphone is usually a metallised plastic foil. An immovable counter electrode is located opposite this movable diaphragm. The two together form a plate condenser (hence the name "condenser microphone").
If a voltage is applied to this construction, the capacity changes when the gap between the diaphragm and the counter electrode changes (i.e. when the diaphragm vibrates), which allows a downstream electronic device to extract the audio signal. This electronic device (and for true condenser capsules the bias voltage that must be connected to both electrodes) also explains why condenser microphones always require a voltage supply to operate, mostly so-called phantom power (or occasionally also a battery).