I will try to answer your question as I understand it. In short, the Wright brothers proved that heavier than air flying machines were possible in principle. Although there is some dispute as to the question if they were indeed the first to fly a motorized heavier than air machine successfully, as there are multiple claims

The long answer places Orville and Wilbur in a longer tradition of the development of the heavier than air aircraft, in which they solved the propulsion and control problem. Both Otto Lilienthal (1848-1896) and Sir George Cayley (1773-1857), to name a few, had conducted experiments with heavier than air gliders in their life time. Their designs lacked two things: an engine light enough to keep them afloat, in their case they traded potential energy for kinetic energy, in fundamentally the same manner as glider aircraft today operate. They started from a high point (Usually a hill) started to run and at some point the airflow over the wing would generate enough lift to become airborne, after which they floated downhill trading altitude for forward momentum all the way down. Note that the problem of lift was thus already solved, however not fully understood. Flying time was practically limited to the height difference between launch and landing point.In order to fly for longer periods energy needed to be added, but mid 19th century the only engines available were steam engines, which had a very poor power to weight ratio and were unsuitable. Another problem that was apparent with Cayley and especially Lilienthal was a lack of control. Lilienthal’s glider designs relied on the shifting of body weight for control. On august 9th 1896 his last design proved to be unstable, sending him into a nose dive from which he was unable to recover.Lacking an application the gliding efforts of Cayley and Lilienthal were more or less forgotten and not followed up on.

What the Wright brothers did was focus their initial attention at what they called the third problem of flying or the problem of equilibrium: control along all three axis. The two other problems they considered already solved in principle: Lift was already proven by Lilienthal and other glider pilots by constructing wings with a hollow profile analogous to the wings of birds. By the late 19th and early 20th century the internal combustion engine provided a more suitable power to weight ratio than steam engines, thereby offering a promising avenue to pursue the power problem. Although it would take them some time to practically apply petrol engines and to construct suitable wings, the principles were already there.

“Wilbur’s observations of birds in flight had convinced him that birds used more positive and energetic methods of regaining equilibrium than that of a pilot trying to shift the center of gravity with his own body….its balance was controlled by utilizing dynamic reactions of the air instead of shifting weight.” (1)

The thinking from the quote above, also inspired by their work with bicycles (in order to steer a bicycle it is necessary to lean (movement along longitudinal axis or roll) rather than just move the steering wheel (Movement along vertical axis or yaw)), led them to think about means of control, which prompted them to experiment with models and kites first. They invented a wingtip warping system which allowed steering by aerodynamic forces, rather than weight shifting. It is no coincidence that their first patent was for a system of aerodynamic control. By contrast, other inventors failed to acknowledge the problem of pitch and roll, and usually just added a rudder for yaw control analogous to the way in which ships were steered. Putting solutions to all three problems together in a working machine is what the Wright brothers did, thus proving that man could take to the air in a controlled manner. What they really added to the development of the aircraft was three axis aerodynamic control. Although wings of modern aircraft in general do not use warping surfaces anymore, they do rely on the same principles first applied by the Wright brothers.

Sources

Wright brothers patent: https://patents.google.com/patent/US821393?oq=821%2c393

David McCullough, The Wright Brothers, 2015 (1) quote taken from p.38. McCullough bases himself on the diaries and notes of the brothers.

J.A.D. Ackroyd, Sir George Cayley, the Father of Aeronautics Part 1&2, Notes and records of the royal society of London, Vol 56, No.2 + No3.