The Yuan Dynasty was the "dynasty" in place in China from 1279 to 1368 CE, during the third empire. Kublai Khan and the Mongol empire took control of China in 1279, and ruled as a Chinese dynasty, rather than as tribal lords.
During this foreign rule, Chinese culture did not suffer as much as it could have, due to the maintainance of the Chinese way of life by the Mongols. Buddhism in particular prospered during this era as the Mongols had more or less adopted it in a relaxed form.
This was also the period during which Marco Polo made his trip and later service to China; during these years the Mongolian Khans also (especially Kublai) supported the courtly debate of religion with Christians, Muslims, Hindus, and Tibetan and Chinese Buddhists. Ch’an ("Meditation") Buddhism was pressured to write down their doctrine in the form of koans, supporting the future development of Zen Buddhism.
The Yuan dynasty represents a very important time for the development of Buddhism, with support coming from the Mongols; the development of Ch’an Buddhism; and courtly, academic, officially supported communication with other popular religions at the time.