The theremin works using the same electric fields formed from static electricity. But instead of charge staying the same, it changes. A Theremin's circuitry adds charge to the antenna at a fixed rate. This charge is used to measure the capacitance between the theremin and the nearby environment.
With only a little bit of capacitance to the outside world, few electric fields form, and the voltage on the antenna increases quickly.
But if you move your hand towards the antenna, capacitance increases. Your hand becomes a place that electric fields can build up. Because the circuit adds charge to the antenna at a fixed rate, it takes longer for the voltage on the antenna to rise. The theremin detects this change in charging time and uses it to control the pitch and volume of the output.
Think of capacitance as a water balloon, and the charge building up as a constant flow of water. Your hand adds capacitance, or makes the balloon bigger. Because of this, it will take longer for the tank to fill up. We will use the idea of electricity flowing like water to explain electronics in more details in the next section.