what is the USB c port for on the back of my AppleTV 4K for?

If your Apple TV model has a USB-C port on the back, then you may have an Apple TV (4th generation), not Apple TV 4K (5th generation).

Identify your Apple TV model - Apple Support

It can be used to connect to a computer with iTunes, to re-install the system software, if you can’t do so on the device itself through the menus.

Restore your Apple TV through iTunes - Apple Support

Apple TV HD; previously known as Apple TV (4th generation).

The USB-C port on the back of the Apple TV is for development or diagnostic purposes. It isn't present on the Apple TV 4K.