What is it? Is this like a gear, where the output shaft turns at some fraction of the input shaft? Is better or worse than traditional toothed gears in some way?

It acts like a gearbox, allowing you to sacrifice rotational speed for higher torque output. What makes this gearbox type special is their low backlash, multiple points of contact, and high efficiency.

They're pretty cool. They can be good in situations where you don't want any backlash and lots of torque. I believe they're very popular as actuators in robotics.