The term "shi'i" is a contraction of the phrase "shi'at Ali." This phrase means "partisans of Ali" or "party of Ali."
Ali was both the cousin of the prophet Muhammad and his son in law. After Muhammad's death, many Muslims believed that Ali should be the next leader of the faith because he was the closest living relative of the prophet. However, he was passed over a number of times before finally becoming the caliph. He was later assassinated. The Shi'ites became a separate branch of Islam after Ali son, Husayn was assassinated in 680.
So, the term "shi'i" comes from the fact that the Shi'ites started out as people who believed that the successors of the prophet should be people who were related to him.
the shi'ites have totally different beliefs that the sunnis do not accept since the sunnis are more faithful to the prophet Muhammad (Peace Be Upon Him).
like the christianity it have three main banches catholic , orthodox and protestat. That is more like what happend to Islam it dividrd anto suni, shi'i and more branches .