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.