The easiest way to think about it is that 1 full rotation (pi radians) in 1 second makes 1 Hz.

The number of rotations made in a second corresponds to Hz in the same way that the number of sine wave periods that fit in a second also represents Hz. This gif does a really good job of showing how rotation relates to sine/cosine waves, which just so happens to help visualize the rad/s -> Hz <- periods/s relationship:

Image