Linguae

To "wait on" someone or something is to be immediately available to answer any need. The term may thus have originally been "to wait on someone's hand and foot", thus meaning to have no other duty but to address any need of that hand and/or foot, be it heat, cold, an itch, or in more general terms responding to its every move including as a gesture having meaning. 😅 Over time the possessive may have been discarded.