The condenser microphone works on the principle that a voltage change occurs over a capacitor (electric condenser was an older name for capacitor) when the capacitance is changed while the charge is constant.

Buildup of a condenser microphone:
M    -----
e    :----
m    :   |
b    :   |
r -- : D | -- metal electrode
a    :   |
n    :---|
e    |---|
     O   O

The membrane is made from a thin foil of conductive material. The dielectrical medium is usualy air. This type of microphone must be connected to a powersource. This is to charge the capacitor formed by the membrane and electrode When a soundwave hits the membrane it will vibrate and the capacitance of the microphone varies, and thus the voltage over it. the voltage variation is an analog representation of the soundwave.
A variation of this microphone is the electret condenser microphone. It has a membrane made of electret. It doesn't need a charging powersource, since the electric field from the electret does this job.

The electret microphone is easier to use and cheaper than the condenser microphone but has a poorer frequency 'reproduction' (it has a lower sensitivity to low frequency sound).

The condenser microphone is used in professional microphones due to bether sound quality than dynamic microphones.