13c., "seagoing vessel having both sails and oars," from Old French galie, galee "boat, warship, galley," from Medieval Latin galea or Catalan galea, from Late Greek galea, of unknown origin. The word has made its way into most Western European languages. Originally "low, flat-built seagoing vessel of one deck," once a common type in the Mediterranean. Meaning "cooking range or cooking room on a ship" dates from 1750.
The printing sense of galley, "oblong tray that holds the type once set," is from 1650s, from French galée in the same sense, in reference to the shape of the tray. As a short form of galley-proof it is attested from 1890.