Properly called strain wave gearing, it has three parts: an oval wave generator, a thin flexible cup with outside teeth (the flexspline) and a rigid outer ring with inside teeth. The oval makes the flexible cup bulge and mesh with the ring at two points; as it rotates, the cup creeps backwards by the few teeth of difference per turn.
The result is a reduction of roughly 50:1 to 160:1 in a flat, light package with very little backlash, the loose play you feel when you wiggle a cheap gearbox. Low backlash is what lets a robot return to the same weld point again and again.
The downsides are cost, some elasticity in the flexible cup and limited backdrivability, meaning you cannot easily push the joint by hand. Harmonic Drive is also a company name; the neutral term is strain wave gear.
