What does the USB-C cable plug into that comes with the Beats Flex earphones? It does not fit any connector in my PC or my IPhone plug. This is crazy!!

A USB-C connector requires a USB-C port. Most USB ports, prior to USB-C, were the USB-A type, which is physically different. If you want to use this plug with your PC, you will need to get a USB-C-to-USB-A adapter.

As far as your iPhone, it has a Lightning port. In this case you would need a USB-C-to-Lightning adapter.