Due to less drag/friction it allows for two things:
1. Lower fly height of the read/write heads over the platters
2. Thinner platters (thus more per drive).
It's the same principles that make your vocal chords run faster when you breath in helium (less friction to contend with, thus faster vibrating). Or in the case of a HDD less overall internal vibration to contend with while writing data at a microscopic level.
The overlapping of tracks that Sveta mentions is called SMR, and actually has nothing at all to do with Helium. In fact current helium drives generally aren't SMR drives, and more current SMR drives are simply air filled. However it's expected that soon the two technologies will both be used together to make for drives in the 12-20Tb range.
Most air filled drives are capped at 4-5 platters, while many helium ones are 8 platters.