In some ways the Mongols were responsible for the united Russian and Chinese state. Before the Mongols, as others have noted the Chinese and Russians were more loose association of states. After banning together and losing to the Mongols, Ghengis Khan was very effective in organizig these loose “tribes” into bands of government.
The Mongols were very effective, because they were ruthless. They would hold entire villages of women and children hostage and burn the entire places to the ground. Mongols were very mobile and this helped them. They would essentially use technology that they didn’t have but got from one conquered people and adapt that warfare technique to mobile operations.
The Mongols moved very swiftly and a favourite technique was to surround a village and starve it out, and after the villagers finally surrendered they would slaughter every inhabitant.
The Mongols most successful technique was to simply refuse to fight any battle they couldn’t win. Many times the Mongols came upon an ememy they knew they couldn’t beat the would simply withdraw.
The Arabs were particularly good at beating off Mongol attacks as they too were nomads and had similar forms of warfare. Ambush, attack, pick off the easy things, retreat, then before the enemy had a chance to regain strength, they’d, ambush, attack, pick off the weakend and retreat again.
But as others have said, the biggest advantage the Mongols had were they were a product of their time. Once the Mongols had established a bloodthirsty reputation, they would go up to a city, demand 10% of its weath and its surrender. Most cities complied.
Why? Because there wasn’t many places with nationalism back then.
You have to look at it this way, suppose you were a serf or a peasant, you paid almost all your income to a local government, who probably couldn’t protect you anyway. If the Mongols came in they took the same amount of taxes from you, so what difference did it make who ruled you. And you might as well be on the winning side.
The Mongols also had a lot of religious toleration, something the Christian and Muslims didn’t have. So it made little different to the peasant if he was ruled by a Mongol or a Christian Ruler or a Muslim Ruler.