The Order of the Hospitaliers of Saint John in Jerusalem, who had adopted the cross of John the Baptist as their emblem, were initially focused on healing Christian pilgrims who had come to Jerusalem (as their name suggested). However, as the Crusades went on, during the early 12th century they were forced to provide more and more of a military role as well, while the Knights Templar - who were charged with the defending the pilgrims - were otherwise occupied with holy relic scavenger hunts.
These "Knights of Saint John" participated in battles which were fought against Saracen who wielded either Greek fire or naphtha bombs. When fire sources were cast into crowds of highly flammable naphtha-soaked crusaders, the Knights of Saint John rescued men who would have otherwise burned to death.*
As conditions in Jerusalem worsened for the Christians, the order eventually retreated to Cyprus in the late 13th century; in 1530, they moved to the island of Malta after receiving it as part of a grant from King Charles V of Spain. The Maltese cross (obviously) derives its name from the island of Malta, as the Knights of Saint John flew flags bearing their emblem there for over 270 years.
*The Maltese cross has been used as an emblem for firefighters since the Knights' heroics in the Crusades. However, the likeness of Saint Florian, the patron saint of firefighters, is a much older symbol which firefighters still use today.