The biggest single hurdle would be the development of a design that has just the right amount of stability while still giving 3-axis control to the pilot, but that was far from the only breakthrough.

The control system was developed of hundreds of kite and glider flights over the previous two years, eventually leading to the system where roll can be controlled by wing warping, and that tied the warping to turning the rudder simultaneously.

In the off-seasons the Wrights methodically developed the other features of their airplane design through extensive wind tunnel experiments. They did many comparisons of lift-vs-drag of wings of varying Aspect Ratio. In other words they found that for the same area, a square wing does not lift as well as a longer narrower wing. They tried a number of different cambers for the wing, eventually settling on a 1/20 curvature for the wing's airfoil. They measured lift in varying angles of attack and found that when the wing is pitched up by 20 degrees it suffered a large decrease in lift, and that you got better lift at 6 degrees.

They were not developing all of this in a (metaphorical) vacuum. They had presented their conclusions from the 1901 glider at a conference. They were in active correspondence with Octave Chanute, and they had studied Lilienthal's and Langley's experiments going back into the 1880s. They went so far as to replicate most of Lilienthal's data, and developed their own conclusions.

There is a nice overview of the development process at http://pcwww.liv.ac.uk/eweb/fst/publications/2854.pdf including an aerodynamic comparison of the 1901 and 1902 gliders.

As to why the development accelerated so quickly in the two decades after the first powered flight.... It's much easier to improve an existing model than it is to come up with the whole thing from scratch. You can build an airplane just like the first and tweak it some and then fly both to compare.