Twelver Shiism holds that leadership after the Prophet belonged by divine appointment to Ali and to his descendants through Fatima, and that the community took a wrong turn at the outset. That is a claim about history, and Shia devotion is organised around the events that followed from it.
The decisive one is Karbala. In 680, Husayn, son of Ali and grandson of the Prophet, refused allegiance to the Umayyad caliph Yazid and was killed with a small party of family and followers on the plain of Karbala in Iraq. The commemoration of that death on Ashura, with mourning assemblies, elegiac poetry, passion plays and in some communities self-flagellation, which many Shia authorities discourage, is the emotional centre of Twelver religious life in a way that has no exact Sunni parallel.
The Imams are held to be twelve in number, beginning with Ali and continuing by designation, and to be sinless, divinely guided and the authoritative interpreters of revelation. This is not a merely political claim: the Imamate is a principle of religion for Twelvers, in the way the prophethood of Muhammad is.
The twelfth Imam is held to have gone into occultation in 874, remaining alive and hidden, and to be the Mahdi who will return with Jesus to fill the world with justice. That absence is the fact around which the whole system of present authority is arranged, because it means no living person holds the Imam's office.
Practice differs at the visible margins: Twelver law breaks the Ramadan fast slightly later, permits a temporary marriage contract Sunnis reject, and combines the five daily prayers into three sittings. Pilgrimage to the shrines of the Imams at Najaf, Karbala and Mashhad sits alongside the Hajj rather than replacing it.