The Wrights made a breakthrough in realizing that a propellor was a rotating wing, and developed the first theory of propellors enabling them to build one that was 90% efficient. This is as opposed to the flat bladed screws used by other experimenters which were 50% efficient.
This means a near doubling of power for the same weight of engine and drive train.
The Wrights could not find an existing engine with the desired power/weight, and the engine makers refused to design/build one. Hence they hired a machinist to help design/build a custom engine, with double the power/weight ration of existing engines. The Wrights developed the very first practical aviation gas engine.
This was an enormous factor in creating a successful airplane.
P.S. Fun fact: Santos Dumont was a rather tiny man. In the movie "Those Magnificent Men in their Flying Machines" they created several flying replicas of early machines, including Dumont's "Demoiselle". But the Demoiselle wouldn't fly, it just ran around the field nailed to the ground. Finally, the engineers realized that Dumont was a tiny man, and located a tiny pilot, and then the Demoiselle flew delightfully. So, Dumont had his own peculiar advantage in power/weight.