The Shia believe in Imams, consisting of Ali (cousin of Prophet Mohammad & husband of Prophet Mohammad's daughter Fatima) and a select number of his descendants. The number and identity of these Imams varies from one Shia sect to another, some of them believe in only 7 Imams while others believe in 12 Imams. The largest Shia sect (known as the Twelvers) believe in 12 Imams who are: (1) Ali, (2) Al-Hasan, (3) Al-Hussain, (4) Zain Al-Abideen, (5) Muhammad Al-Baqar, (6) Jaffar Sadiq, (7) Moosa Kazim, (8) Ali Al-Ridah, (9) Al-Taqi, (10) Al-Naqi, (11) Hassan Askari, and (12) Al-Mahdi.
The Shia believe that the final Imam, called Al-Mahdi, disappeared hundreds of years ago and went into occultation state, but he will re-appear around the end of the world, before the Day of Judgment. Shia's Al-Mahdi is very different in his characteristics from Al-Mahdi that prophet Mohammad mentions that he will appear to lead the Muslims at the end of time. Shia's Al-Mahdi based on what the Shia's reference books mention seems to be more like a Prince of Vengeance who will take revenge against the Sunnis, he will bring back to life, crucify and torture, Abu Bakr & Omar (Prophet Mohammad's closest companions) and Aisha (Prophet Mohammad's wife).
Shia's Imam Mahdi is a fictitious, imaginary character. He never existed as a child. He does not exist now, contrary to what they believe. Therefore, there will never be any person appearing in the future who will fulfil all the characteristics and signs of Shia's Imam Mahdi. Some Shia may follow the Anti-Christ, thinking he is Shia's Imam Mahdi because there are many similarities between them (click here for an in-depth analysis of this point).
The Shia believe that the Imams have a divine mission, to rule the Muslims after Prophet Muhammad (s.a.w.), and represent God on Earth. They claim that knowledge of the unseen belongs solely to their Imams, and it is not for the Prophet to inform us about the unseen.
Some Shia have gone so far as to claim divinity for those Imams.
[4:59] O you who believe! Obey Allah and obey the Messenger (Rasul) and those in authority (Ulil-Amr) from among you; then if you quarrel about anything, refer it to Allah and the Messenger, if you believe in Allah and the last day; this is better and very good in the end.
As you can see, the obedience to Rasulullaah ("the Messenger (of God)") is equal to the obedience to Ulil-Amr ("the people of authority") as can be seen by the wording.
One of the reasons why we trust Rasulullah and we have to obey him is because his words are not his own; they are the words of God (69:40-47). He receives communications from the Lord Almighty. He is infallible. The same must apply to Ulil-Amr because they must be obeyed without condition. Since the verse equates the obedience to the Prophet to the obedience to the Ulil-Amr, one cannot disobey the Ulil-Amr.
Notice that the verse says "if you quarrel about anything, refer to Allah and the Messenger"; since we cannot disobey the Ulil-Amr, even when we quarrel with Ulil-Amr, they cannot be in the wrong.
In one verse, the Ulil-Amr are given nass (designation), authority, isma (infallibility), and ilm (knowledge). Let's give the Ulil-Amr a nickname. How about "Imams"? Oh wait, that sounds suspiciously like the Shia concept of Imamate. Plagiarism perhaps lol? Or maybe the same Author is behind this all.
"I asked Abu 'AbdAllaah (as-Sadiq) (???? ??????) about the words of Allaah (????? ?? ?????): 'Believers, obey Allah, His Messenger, and your leaders (who possess Divine Authority). . . .' (4:59) "The Imam said, 'This was sent from the heavens about `Ali ibn Abi Taalib, Al-Hasan and Al-Hussain (???? ??????).' I then said, 'People say, "Why did He not specify Ali and his family by their names in the Book of Allaah (????? ?? ?????)?' "The Imam said, 'Say to them, "The command for prayer came to the Messenger of Allah but He has not specified (the number of the Rak'ats) for them as being three or four. It, in fact, was the Messenger of Allah who explained to them this matter. The command for Zakat (a form of income tax) came to the Messenger of Allah and there was no specific taxable number such as one Dirham on every forty Dirham. It was the Messenger of Allah who explained it for them. The command for Hajj came to the Messenger of Allah. It did not say walk seven times around the Ka'ba. It was the Messenger of Allah who explained it for them...."
Source: al-Kulayni in his al-Kafi, volume 1, pages 286?288, hadeeth #1
Grading: al-Majlisi said this hadeeth is SaHeeH (authentic) in his Mir'aat Al-`Uqool, volume 3, page 213.
That is a short summary, also, the word "Imam" in Arabic is mentioned 12 times in the Qur'an. And if you know anything about the mathematical miracles of the Quran, you should know this too is not a coincidence.