Ap human geography? Ahaha, i just studied this in the class. Basically the two major branches of Islam are the Sunnis and the Shi'ites. Shi'ites believe that Islam should be led by descendants of Muhammad, while Sunnis believe that the leader of Islam should be appointed by election and consensus. Sunnis make up 84 to 90 percent of the world's Muslims. The word Sunnirefers to the words and actions of Muhammad. The Sunnis try to follow Muhammad's example of how to live as a Muslim. This is the relationship between the two branches then, and now, it's still the same.
As for the reason why they split, is because they have different opinions on who should be the leader of Islam.
Hope that helped you!