How did Mongol empire gain control of such large territories

There were several reasons behind Mongolian military success.

They were nomads. And relied mainly upon cavalry tactics to win wars while many of the other Asian and European nations relied upon heavy infantry and non flexible military tactics.

The Mongolian cavalry and cavalry archers turned the tide of many battles.

Moreover, during this period Europe was in the middle ages or the dark ages and went through severe social, economic and political problems in their nations, destabilising their countries and the military.

But the most significant reason behind the mongols overwhelming many nations and militaries at that time was their superior and flexible cavalry strategies.