1620s, "act of carrying or conveying," from Late Latin convectionem (nominative convectio) "the act of carrying, a carrying or bringing together," noun of action from past-participle stem of Latin convehere "to carry together," from assimilated form of com "with, together" (see con-) + vehere "to carry" (from PIE root *wegh- "to go, move, transport in a vehicle").
Specifically of the transference of heat or electricity through change of position of the heated or electrified body (distinguished from conduction) is from 1834. Related: Convective. Convection current recorded from 1868.