Many Muslims and non-Muslims alike believe that the Sunni/Shia divide was based upon a theological disagreement. Many hold the mistaken belief that Sunnis believe the elder should be the next leader of Islam, while Shias believe the Prophet's son-in-law/cousin should be the next leader (blood relation).
The vast majority of muslims and non-muslims believe some version of the above statement. That it was a disagreement over theology, or that it was a political disagreement. This is simply incorrect.
The disagreement can be boiled down to simply: Shias believe the Prophet Mohamed (PBUH) declared a successor and that was Imam Ali (PBUH), while Sunnis believe the Prophet (PBUH) died without a naming a successor.
Shia can point to many narrations in history that show the Prophet named a successor directly (Imam Ali PBUH), and also talked extensively about his successor before he named him.
Sunnis are told by their local sheiks that there was never a successor named, and the people chose Abu Bakr, the eldest companion of the prophet (PBUH) to be the successor. However, both narrations are incorrect. Sunni's own history traditions don't support either of these assertions. However this is a subject for another post.
The remaining differences between sunnis and Shias are very minor. However, through time, these minor differences have resulted in substantially different cultures and practices as we see today. This again is a subject for another post.
