What is the role of the Imam's in Islam how they become Imam (is it by God or by their knowledge)?

Praise be to Allah, the Lord of the Worlds; and blessings and peace be upon our Prophet Muhammad and upon all his Family and Companions.
As for Imams and their role in Islam if you mean the great Muslim Imams headed by Abu Bakr, Omar, Uthman, Ali, Ibn Massoud, Ibn Abbas, Mouaz Ibn Jabel () and other companions of the Prophet as well as the scholars of Islam who came after them like Abu Hanifa, Malik, Ahmad, Al Shafie, Al Thowri, Al Bukhari, () ….etc. if you mean these, they are among the rightly guided and most prominent Muslims. Allah Says (interpretation of meaning) about the children of Israel: "And We made from among them (Children of Israel), leaders, giving guidance under Our Command, when they were patient and used to believe with certainty in Our Ayât (proofs, evidences, verses, lessons, signs, revelations, etc.)." [32:24] The Imams are indeed the leaders who give guidance under the Command of Allah.
Imama (state of Imam) is a position which is reached by the most pious, the most patient and the most knowledgeable among Muslims.
So, any scholar who does the mission assigned by Allah to Imams which is to teach people the true religion and guide them to the right path is an Imam.
But if you mean by Imam, the so-called twelve Imams who are hallowed by some deviated groups claiming that they (these twelve) are infallible, while only Prophets are infallible, know that this claim is false and untrue. There is nothing in the Qur'an or the Sunnah about these "Twelve". In fact, the Muslim Ummah is full of people who are better than they such as Abu Bakr, Omar and the ten people whom the Prophet said will go to Paradise.

Allah knows best.