Differences between the majority Sunni and minority Shia Muslims date back to the very earliest days of Islam. They are directly linked to the issue of succession following the death of Prophet Muhammad.
The Shia believe that after Prophet Muhammad's death, his son-in-law, Ali, should have been given the reins of administration. They still regard him as the first imam or spiritual leader.
The Sunni, however, believe that the appointment of one of the Prophet's companions, Abu Bakr, as the first caliph was correct.
See : The early Caliphs
The Great Schism
Mo'awiya laid the foundation of family rule in Islam and he was later succeeded by his son, Yazid. But Ali's son Husayn refused to accept his legitimacy, and fighting followed. Husayn and his followers were massacred in Battle in Karbala in AD 680.
The deaths of both Ali and Husayn gave rise to the Shia characteristics of martyrdom and a sense of betrayal. Even today, Shia all over the world commemorate the killing of Husayn with vast processions of mourning in Iran and other parts of the Muslim world.
Today, the Shia make up about 15% of the total worldwide Muslim population. The Shia are a majority in Iran (89%) and in Iraq (60%).
www link :
Encyclopedia of Islam