There had been an enormous amount of research into aeronautics in the previous decades, even the previous hundred years. Gustav Eiffel had built a wind tunnel for experiments. Otto Lilienthal had worked out the advantages of curved wing surfaces, Samuel Pierpont Langley had come up with instruments for measuring aerodynamic forces. By the time the Wrights began to work, Octave Chanute could supply them with a lift and drag coefficients for wings of various flying machines. The Wrights could test Langley's airfoils in their wind tunnel.

So, a lot of important stuff had been figured out. How to make wings, that lifted. There were propellers, and though not very efficient, they worked. There had been some early airplanes that could lift, hop , fly a distance before they came down. The Wrights came up with most critical piece: how to control flight. They also invented with a more efficient propeller, and came up a lighter aluminum engine to power it. But control- with the inventions of ailerons- was the last bug hurdle. At that, the basic aircraft building blocks were known. And once those building blocks were known, everyone could begin building things that flew ( or, at least, everyone who was not within easy reach of the Wrights' patent lawyers). And once people could get planes into the air and stay there, it was much easier to figure out how to make them work better and better ( for one thing, people didn't think you were crazy for tinkering with flying machines anymore). In 1909, Louis Blériot built something to fly him across the English Channel. Four years later he was the head of a company that made planes; three years after that it was making the famous SPAD fighter ( after the initials of the company, Société Pour L'Aviation et ses Dérivés) , one of the most famous fighter planes of WWI.

And of course it's not like things stopped at WWI. By 1930, B. Melville Jones had worked out how important streamlining would be, that a properly designed plane could very efficiently fly hundreds of miles per hour, and almost immediately the "string bag" biplanes were obsolete and the aluminum-skin monoplanes were there. Aeronautics and airplane design really did move incredibly quickly in the first decades.

One thing I'll add here that hasn't been mentioned is that the airplane had its early period of rapid progression precisely when automobiles were experiencing a similar effect, and not entirely coincidentally either. For both technologies advancements in the state of the art of lightweight high power internal combustion engines were key enabling innovations.

When the Wright Brothers first flew automobiles were still "horseless carriages", there were few of them, and they were generally open cabin. By 1911 there were over a million automobiles worldwide, the Model T was in production and cars were starting to look more and more like what we're familiar with. Add to that similar rates of adoption and innovation in internal combustion powered tractors and trucks. More importantly for airplanes, engines started getting much better very rapidly. Between the first and third Wright Flyers they went from 12 to 20 horsepower, but by 1911 there were planes with 75 to 100 hp (like the Fokker Spin). By WWI engine power had grown even farther, into the 150 to 250 horsepower range per engine, with some aircraft having multiple engines, over 40x greater than what the Wright Brothers originally had flown with.

More horsepower means you can bring up more weight, which means you can do more stuff (like guns and bombs). It also means, potentially, more control authority and more speed (over 100 mph for many WWI planes, compared to the 30 mph for the first Wright Flyer flight).