1848, "to throw overboard," especially to save a ship in danger, from jettison (n.) "act of throwing overboard" to lighten a ship. This noun was an 18c. Marine Insurance writers' restoration of the earlier form and original sense of the 15c. word that had become jetsam, probably because jetsam had taken on a sense of "things cast overboard" and an unambiguous word was needed for "act of casting things overboard."
Middle English jetteson (n.) "act of throwing overboard" is from Anglo-French getteson, Old French getaison "act of throwing (goods overboard)," especially to lighten a ship in distress, from Late Latin iactationem (nominative iactatio) "a throwing, act of throwing," noun of action from past participle stem of iactare "to throw, toss about" (from PIE root *ye- "to throw, impel"). Related: Jettisoned.