hospitalyoudaoicibaDictYouDict
hospital: [13] Like hospices, hostels, and hotels, hospitals were originally simply places at which guests were received. The word comes via Old French hospital from medieval Latin hospitāle, a noun use of the adjective hospitālis ‘of a guest’. This in turn was derived from hospit-. the stem of Latin hospes ‘guest, host’.

In English, hospital began its semantic shift in the 15th century, being used for a ‘home for the elderly or infirm, or for down-and-outs’; and the modern sense ‘place where the sick are treated’ first appeared in the 16th century. The original notion of ‘receiving guests’ survives, of course, in hospitality [14] and hospitable [16]. Hospice [19] comes via French from Latin hospitium ‘hospitality’, another derivative of hospes.
=> hospice, hospitable, host, hostel, hotel
hospital (n.)youdaoicibaDictYouDict
mid-13c., "shelter for the needy," from Old French hospital, ospital "hostel" (Modern French hôpital), from Late Latin hospitale "guest-house, inn," neuter of Latin adjective hospitalis "of a guest or host," from hospes (genitive hospitis); see host (n.1). Later "charitable institution to house and maintain the needy" (early 15c.); sense of "institution for sick people" is first recorded 1540s.