Theremins use capacitance to sense the world around them. Capacitance is the measure of how easy it is to store energy between two objects in the form of electric fields. You’ve interacted with electric fields if you’ve ever felt static electricity from a nearby object. If you rub a balloon on wool, it creates a negative charge on the balloon and an equal positive charge on the wool.
When you move the two objects far apart, they are still charged. But because of the distance, electric attraction is weak. From far apart, the wool and balloon barely interact.
But move the wool close to the balloon, and the two objects will attract each other. They have the same amount of charge as before, but the attraction is stronger. This is because there is more capacitance between the objects. When two charged objects move closer together, it is easier for electric fields to form between them.
Capacitance also depends on the size of an object. If an object is half the width, only half of the electric fields will form, halving capacitance. The exact shape of the two objects and the material between the two objects also affect capacitance.