Imamah (Divine Leadership) is what makes Shi'a Islam unique in comparison to other schools within Islam.
Shi'a Islam maintains that the office of the Imamah is a divine office - meaning, the Imam or Khalifah (leadership) has to be appointed and given directly by Allah.
People are thus commanded by Allah to follow specific successors (Imams) after the demise of the Prophet (pbuh).
"And remember when the Lord of Abraham tried him with certain commands which he fulfilled. Allah said to him, ‘Verily I am going to make you a leader (imam) for mankind.’ Abraham said, ‘And (what about) my offspring?’ Allah said, ‘My providence (does not) includes the wrongdoers." (2:124)
Numerous verses in the Noble Qur’an refer to the fact that throughout history Allah alone has the right to ordain an imam (leader) or khalifah for mankind.
A clear example is the above verse regarding Prophet Abraham (as). There are numerous other verses too - some of them are as follows:
Verses of Imamah
And remember when your Lord said to the angels, ‘Verily, I am going to place [for mankind] a successor (Khalifah) on the earth.’ (2:30)
O David! Verily We have placed you as a successor (Khalifah) on the earth, so judge between men with truth and justice, and follow not your desires, for they will mislead you from the path of Allah. (38:36)
"And We made from among them leaders (Imams), giving guidance under Our command, when they were patient and believed with certainty in Our proofs and evidence." (32:24)
It is Allah’s wish to remove all blemish from you, O Ahlul-Bayt, and purify you with a perfect purification. (Qur’an 33:33)
Say, I ask no reward from you for it except the love of my kinsfolk. And whosoever does a good deed we add unto it a greater good for him. Lo, Allah is Forgiving, Responsive. (Qur’an 42:23)
And whoever disputes with thee concerning him after the inspired knowledge which has been given unto thee, tell him, "Come, let us call our sons and your sons; our women and your women; and ourselves and yourselves; then let us pray and invoke Allah’s curse upon those who lie.”(Qur’an 3:61)
Hold fast to the Rope of Allah, all of you together and do not diverge. (Qur’an 3:103)
Be careful of your duty to Allah and be with the Truthful. (Qur’an 9:119)
Lo, this is My Straight Path, so follow it and do not follow other ways or else you will diverge from His way. (Qur’an 6:153)
O you believe, obey Allah and obey His Messenger and those amongst you who are give supreme authority (by Allah). Qur’an (4:59)
Whoever opposes the Prophet after the guidance has been made manifest unto him and follows any path other than the path of the true believers, We will turn him towards that unto which he himself has turned, and We will expose him to Hell and a bad journey it will be. Qur’an (4:115)
(O Prophet) Lo! thou art a warner and for every community there is a guide. (Qur’an 13:7)
Guide us in the Straight Path: The Path of those whom Thou hast blessed... (Qur’an 1:6-7)
They are those whom Allah has blessed among the prophets and the verifiers, the martyrs and the righteous. (Qur’an 4:69)
They (i.e., prophets and Imams) do not say anything until He orders, and they act (in all things) by His command. He knows what is before them and what is behind them and they (i.e., those saints) offer no intercession except for anyone whom Allah accepts, and they are in awe and reverence of His (glory). Qur’an (21:27-28)
Verily your master is only Allah, and His messenger and those among the believers who establish worship and pay the poor due while they are bowing down in prayer. Qur’an (5:55)
And lo! Verily I am the Most forgiving towards him who repents and believes and does good and then follows the guidance. Qur’an (20:82)