What really stopped the Mongols at Ain Jalut?

Not one thing, but a well-laid trap and a crisis inside the Mongol family. The battle of Ain Jalut, fought on 3 September 1260 in Galilee between the Bahri Mamluks of Egypt and the Mongol Ilkhanate, marks the first major halt to Mongol advances. Hulegu had sent envoys to Cairo demanding that the Mamluk sultan Qutuz surrender Egypt. Qutuz killed the envoys and displayed their heads on a gate of Cairo.

Then luck turned. In 1259 the Great Khan Möngke died while campaigning against the Southern Song, and Hulegu went back to Mongolia with the bulk of his army for the kurultai, leaving about 10,000 troops under Kitbuqa. Qutuz marched into Palestine. The Franks of Acre stayed neutral and supplied his army. At Ain Jalut the Mamluks knew the terrain: Qutuz hid most of his force in the highlands and used Baibars to bait the Mongols. Baibars fought with hit-and-run tactics, then feigned a final retreat. Kitbuqa did not suspect a trick and followed with all his troops into an ambush. Kitbuqa and almost all the remaining Mongol army perished.

The Mongols did not simply lose and leave. Hulegu could not bring his full power against the Mamluks to avenge the defeat, because conflict inside the family got in the way: Berke Khan of the Golden Horde had converted to Islam and was horrified by the destruction of the caliph, and in 1263 the first open war among Mongols signaled the end of the unified empire. Some historians add other explanations, such as the defection of the Mongols' Syrian allies or a climate anomaly after the eruption of the Samalas volcano. The victory was a Mamluk triumph, with a dark ending: on the way home Qutuz was assassinated by emirs in a conspiracy led by Baibars.