What was the main reason for the Mongols' success?
I would argue that there were two main resons for the success of the Mongols in creating and maintaining their empire.
Their success in creating the empire came from their military prowess. The Mongol military included both heavy and light cavalry whose abilities and tactics were beyond those of the people who the Mongols conquered.
But conquering the empire was not the whole story. The Mongols were also good at maintaining it. This happened because they strictly enforced laws that actually helped the people of their empire. They made trade much more easy and managed to suppress things like tribal warfare that had made people's lives hard. They allowed people to practice their own religions instead of imposing a religion on anyone. They even had a fairly flexible system of local governments that could adapt to local conditions.
So, the Mongols succeeded by having a stronger military, but also by doing things that improved the lives of the people they ruled.
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Cohesion. At first, your question is daunting; the Mongols have done many things well, and to pick one to be the main reason for their success across all of their history may seem hard. Though once you begin analyzing the periods where they met with the most success, one should start to notice that it was always made possible by their uniting under, near-unanimously selected, leadership.
The astronauts at the International Space Station can speak to the ancient fear of the Eurasian steppe nomads. After all, they can see evidence of it to this day with the naked eye from low earth orbit. The ancient Great Wall of China stretched for nearly 4,000 miles, across some very mountainous terrain, each mile erected with the goal of keeping the steppe tribes at bay. Just as the peoples who inhabited ancient China knew the danger of the nomads though, they also knew the best way to avoid them was not the wall they were constructing. They always meet with the best success through their foreign policy. The administrations of various ancient Chinese states spent much time and treasure ensuring that the different tribes of the steppes stayed busy fighting each other for power, rather than joining together and looking outwards for plunder or conquest. For long periods of time, effective bribes and tentative alliances were formed with the right tribal leaders in an ever-changing game with the goal of working against whichever tribe happened to appear the strongest at the time. In this way just as one tribe would seem poised to unite multiple tribes into a larger organization, the other tribes would gain needed support from the Chinese states of the time and start to bring down the leading contender among them.
Mongolian military prowess is one of the first things that many think of when they think of Mongolian success. If you look at history as a science experiment though, their strength appears to be a constant, rather than a variable. From the Hunnic invasions of the Roman Empire to the Scythian devastation of the Assyrian Empire, to the Mongol annihilation of the Khwarazmian Empire and eventual complete conquest of China, history is full of examples of how mobile cavalry archer forces were almost unstoppable when in well led and coordinated groups. What of the periods between such conquests? The Mongols and their mounted relatives did not lose their talents for mounted marksmanship when they fought against one another instead of the outside world, and they did not forget how to hunt the animals their tribes subsisted upon in peacetime with such cunning. If they were always so martially skilled that they could pose an existential threat to neighboring settled civilizations, what is to blame for the periods where the Mongols met with little or no success? Of course, here I am assuming that expansion and conquest are the metrics of success.
The answer, as young Temüjin Borjigin realized in his youth, was that the tribes in the area around modern Mongolia must unite and form one entity to become a real threat to anyone. The goal of unification took him the majority of his life, but once complete the steppe tribes declared him "Genghis Khan," or firm/universal ruler, of multiple tribes which we now refer to collectively as "Mongols." From then on him and his descendants met with much success in striking out at the rest of the world until they slowly forgot what he had taught them about thriving as Mongols. Some sources credit him with a quick lesson to his sons and heirs towards the end of his life which showcases the answer to your question and still provides a leadership lesson to this day.
He sat with them and brought out a quiver full of arrows. He held out one, a hand at each end, and snapped it across his knee. He then took out the ones that remained, and in similar fashion tried to break them all across his knee at once. This time though not a single shaft broke. He famously went on to tell them that if they were to remain successful, they must stay together and support each other as the arrows in a bundle. If they were to separate and work singly or against one another, they would be easy to snap like a single arrow. He believed and spent his life showing how the main reason for Mongolian success was their cohesion.