Why did the Islamic Empires and the Europeans lose to the Mongols?
The Mongols' military strength is said to have come from two sources: skill and organization.
The Mongols were extremely skilled with horses and at archery. Because they were so good with horses they had a great deal of mobility, which is crucial in military actions. Their ability to use bows very effectively from horseback made them very dangerous to their enemies, who had only infantry and fairly heavy cavalry (like knights).
The Mongols were also very well organized and disciplined. Their leaders set up systems by which they could coordinate the actions of large groups, even over long distances. The ability to coordinate attacks and other moves gave them a huge advantage over their enemies who were much less organized and therefore less effective.