Well, when the Prophet Muhammad (PBUH) died, there was an argument over who was the next ruler. Half the people thought to elect his best friend, Abu Bakr, who was very knowledgeable as the leader while the other half wanted his son-in-law Ali (RA) to be the ruler, because he was married to the Prophets daughter Fatimah. The Muslims were split. The Shiite's also have different religious views than the Sunni's. The Shiites felt that the rulers of Islam should stay on the bloodline. However, Sunni's do not believe in this, as voting is encouraged in the Shariah (Islamic law) when choosing leaders. Sunni's do not think that rulers should be appointed due to the bloodline. They Shiites pray differently than the Sunni's, too. They also have other festivals that the Sunni's do not celebrate, like the Prophet's birthday.
So you see? This entire disagreement is because Ali wasn't chosen to be the first Kalifah (even though he was the 3rd Kalifah, after Omar (RA))