What advancement did the Sturmey-Archer three-speed hub offer in 1902?

It allowed the rider to select between three ratios without stopping rotation.

The Sturmey-Archer three-speed hub, introduced in 1902, represented a major technological leap in internal gearing mechanisms. Before this development, shifting gears often required the rider to halt the bicycle completely, making momentum management difficult, especially on slopes. The key innovation of the Sturmey-Archer hub was its ability to allow the rider to smoothly select between the three available internal gear ratios while the bicycle was still in motion. This capability significantly improved general utility cycling and provided a substantial advantage over earlier, cumbersome two-speed systems, although it still contrasted with the external shifting concepts being developed concurrently.