First applied to those whose duty it was to provide hospitium (lodging and entertainment) for pilgrims. The most noted institution of the kind was at Jerusalem, which gave its name to an order called the Knights Hospitallers. This order was first called that of the Knights of St. John at Jerusalem, which still exists; afterwards they were styled the Knights of Rhodes, and then Knights of Malta, because Rhodes and Malta were conferred on them by different monarchs.
“The first crusade ... led to the establishment of the Christian
kingdom of Jerusalem, in 1099. The chief strength of the kingdom lay in
the two orders of military monks—the Templars and the Hospitallers
or Knights of St. John.” —
Source: Dictionary of Phrase and Fable, E. Cobham Brewer, 1894
More on Hospitallers from Fact Monster: