During the early days of photography negative size was much more important than now because of the grain size and thus enlargement limitations. Larger negatives meant sharper pictures plus the added benefit of contact printing with is printing photos without having to enlarge it.
In 1932 Kodak introduced two new negative format, 620 and 616, the latter being 70 mm wide. The 616 format was the same as the existing 116 film format but the negative stock was wound on smaller spools in order to fit smaller cameras, that was, at least officially, the reason for introducing yet another format. The real reason might have been that Kodak owed the patent for this roll size and thus was the only one selling film for this format and when you already own the camera, you need fitting (Kodak) film too, right?
The first “6” comes from “6 pictures per film”. Later versions were longer and 8 pictures would fit on the film but the name remained the same. This film format lasted up to 1984 when it was discontinued.
If you respool 120 film onto 116/616 spools, 120 film can be used with cameras designed for 116 and 616, as can 70mm film. When developing, remember to ask the lab for your 116/616 spools back or they’ll be thrown away.