The Shia Imam refers to the Imamate of the Shia sect of Islam. The Imam is considered to be the rightful sucessor to Muhammad, and is similar to the Caliph in Sunni Islam. Unlike the Caliph, the Imam must be descended from Muhammad, through his daughter Fatima Zahra and her husband Ali. This belief is what led to the split between the Shia and Sunni, as the Shia felt that Ali was the rightful sucessor of Muhammad, while the Sunni felt that it was Abu Bakr.
Within Shiism there are various sects that differ over the number of Imams, or path of sucession. The issue of who is the rightful Imam has led to the growth of numerous sects within Shiism including: Ismailis (Seveners), Zaidis (Fivers), Alawites, Druze, and others.
According to the majority of Shia, or the Twelvers, the following is a listing of the rightful sucessors of Muhammad according to their beliefs. Each Imam was the son of the previous Imam, except for Hasan and Husayn who were brothers and both sons of Ali. All the Imams after Husayn are his descendents.
The Zaidis believe that the first four Imams listed above are the rightful sucessors of Muhammad, but differ beginning with the fifth. The Zaidis believe that Zayd bin Ali, and not his brother Muhammad al Baqir was the rightful sucessor to the Imamate. The Imamate for Zaidis is thus transferred from Zayd bin Ali to the other Imams who followed him, they often took the title of caliph. Interestingly, the Zaidi caliphate was not hereditary, but the caliph has to be descended from Ali.