Whenever we use the word Shi`ah, [Shia] we are referring to a group of people who are the followers of Imam 'Ali (may Allah be pleased with him) and they show full fidelity to Aal' Bayt (the household of Prophet Muhammad). Such fidelity is required of all Muslims, and this is pursuant to many Qur'anic verses.
Allah Almighty says, (Allah's wish is but to remove uncleanness far from you, O Aal' Bayt, and cleanse you with a thorough cleansing.) (Al-Ahzaab 33: 33)
Also, there are many hadiths that urge Muslims to give due regard to the household of the Prophet (peace and blessings upon him). For example: "Fear Allah concerning my household (by giving them due regard)", said the Prophet three times. (Reported by Muslim)
However, some people have gone to extreme in showing fidelity to Imam `Ali to the extent that they deify him. Others claim that he was supposed to be the last Prophet as Gabriel mistakenly brought the revelation to Prophet Muhammad (peace and blessings be upon him).
Some of them adopt the idea that Prophethood is co-ownership between the Prophet (peace and blessings be upon him) and `Ali whom they take as deserving the caliphate directly after the demise of the Prophet (peace and blessings be upon him). This follows their claim which they consider to be an implicit authorization from the Prophet (peace and blessings be upon him) himself. Thus, to them, `Ali and his descendants have the sole right to the caliphate and not Abu Bakr, `Umar or `Uthman, and that it is a great injustice of the Ummah to deprive `Ali and his offspring of this right.