It can be used to control an instrument or some parameters of this instrument, like the filters or whatever.
I won't go deeply into the mechanism of the instrument because I am not a specialist and you will find a lot of docs on the internet.
But to make it simple, it use an antenna which produce a frequency and your body will change this frequency. What you get is the difference between the original frequency and the current one. This difference vary with the distance so you can use you hands without touching the instrument to control anything.
For some use you might also want to get the percussions on your instrument, so you can use a Piezo-electric sensor to get them (percussion part in the video).
Step 1: Build the theremin
If you followed the tutorial. You should have connected the Arduino to your computer and run the Adruino code they give. Instead of this code you can use mine. It is the same except that I have commented all the serial communication we don't need, it will just send the distance information.
Run it and on the Arduino application and watch the datas you receive. To do that click on the button up right. Be sure they match the distance of you hand from the antenna. At some point the values are inverted, this is normal and this is also something to improve.