How does a theremin work?

The sound is produced by the interaction of two radio frequency oscillators which normally are operating above the range of human hearing. However, if one of these oscillators is slightly detuned by varying it's frequency while the other oscillator remains fixed, the difference in the frequencies (known as the beat frequency) is in the audible range and can be amplified. This process is known as heterodyning.

The vertical pitch antenna controls the variable oscillator. The electromagnetic field which surrounds the pitch antenna can be changed by the proximity of the human hand, body, or other object placed within proximity of the pitch antenna. The human body possesses a stored electrical charge, which is called its capacitance. This body capacitance can disrupt the electromagnetic field of the pitch antenna, thus affecting the variable oscillator. The closer the hand gets to the antenna, the greater the effect, and, therefore, the higher the beat frequency and the higher the pitch. The farther the hand gets away from the antenna, the less effect of the body capacitance, and, therefore, a lower beat frequency and lower pitch.

The pitch range (tessatura) can be adjusted for four, five, or sometimes more octaves. In addition the pitch can be tuned to allow for variations in playing distance from the pitch antenna (and thus the physical space between pitches) by increasing or decreasing it's sensitivity to body capacitance.

The horizontal volume antenna, which is in the shape of a loop, also controls a high frequency oscillator, which when detuned by the proximity of the player's hand capacitance, lowers the sound volume. Moving the hand away from the volume antenna raises the volume. Carefully controlled up-and-down movement of the left hand (although the antennas may be reversed for left-handed thereminists) helps in the articulation of discrete notes as well as playing dynamics, crescendos, decrescendos, etc.

http://www.theremin-saw.com/theremin.htm

I always saw the flaming lips using it. and they use their hands to block and move the frequency waves creating different sounds.