A Jihad, literally meaning "struggle" is an Islamic holy war which can be declared by a high-ranking Imam. It only appears in Medevial and Medieval II: Total War It is very similar to its Christian opposite, a Crusade, but differs in two key ways. Firstly, as there is no Islamic religious judiciary like the Pope, it does not require the inquiring faction to be aligned with the goals and wishes of any Islamic ruling body. Secondly, the forces of a Jihad may be used against another Islamic nation with no repercussions.
Otherwise, the two systems work in an identical fashion; when a Jihad is called, a family member or general with enough soldiers may join the Jihad and recruit the special mercenary Jihad warriors that become available. Other Islamic factions may join in the Jihad, and compete to take the target city first. When the target settlement is captured, all units involved in the Jihad -- including those not involved in the taking of the target -- will gain an experience bonus.