'How/why' does a human act as a capacitor for a theremin?
The theremin itself does not have capacitance, it responds to changes in the capacitance between the antenna and ground.

Humans consist for a large part of salty water. Making humans electrically conductive. Moving parts of this conductor (your hands) closer to the antenna changes the capacitance I just mentioned and the Theramin responds to these changes.

But there's no wire to ground ??

Correct but usually such a device is powered from the mains which provides it with sort of a connection to "ground". It does not even need to be a real ground connection, a capacitive coupling (any mains supply will have that) is enough to detect the changes near the antenna.