I purposely left it broad because I'm very interested in many aspects including but not limited to, military, economic, social, and political.
I don't know much about the Mongols themselves, but there was an interesting folk legend among European Christians at the time called Prester John.
Prester John was supposedly a Christian king in the Orient whom the Crusaders believed would one day come to the West's aid against the Muslims. This was one reason that the Crusaders sent ambassadors to Genghis Khan, hoping that he was this Christian king come to be their salvation.
Obviously they were disappointed to discover he was as interested in conquering their territories as he was the Muslims'.