The Crusader States are the remnants of European forces which didn't go back to their home countries at the end of the Second Crusade, a conflict that originated between the Byzantines and the Abbasid Caliphate. When, in the 1040's it was obvious the conflict was not going to go away quickly, European nations which had intervened were forced into thinking of a mid-long term plan. Some decided it would be better to leave, and did before the recognised end date of the war. The remainder however decided to leave a presence behind and establish some form of colonial council to monitor them. The Byzantine Empire, left broken and still under the whim of those that came to its aid, was forced to house and feed these armies that remained.
Not all the soldiers did remain however, most went back to their families, businesses or whatever they had back home not wishing to remain in foreign land any longer after the ordeal. Others, given the option of a often reduced rate of pay but better deals on what they could take or do to the "spoils" of raids remained and set garrisons for a prolonged stay.
Of these states, one was formed by the Normans, still maintaining a Government between the Papal States and the Fatimids. The Remnant War would be the continuation of the Second Crusade, famous for its pillaging more than its battles.