What did they mean at the Rep Debate, the '12th Imam'? What's that?

Answer 1

This relates to the belief of the Twelver Shiites (a subgroup of the Shiites) that the 12th Imam, Muhammad al Mahdi, will come again at the end of history to lead the the faithful through several years of chaos; after this he will reign over a harmonious Muslim world.
It is said he went into hiding as a child in the 13th Century, due to political turmoil; he has remained hidden in the caves since then, and will emerge at the right time.
Some Shiites believe that time will be soon. Ahmadinejad of Iran is planning for his return.
He is also known as the Hidden Imam and the Hidden Mahdi (Guided One).