The normal explanation is this:
There are two signals, one which is directional and rotates through 360 degrees around the VOR and the other which issues an omni-directional signal when the rotating signal is pointed towards 360.
Your receiver detects the omni-directional signal, which indicates the rotating signal is pointed North, and starts a clock. When it detects the rotating signal, it checks the time elapsed since it received the omni-directional signal and, using a known rotation rate, it figures out many degrees the rotating signal rotated in the elapsed time, which determines which radial the aircraft is on.