late 14c., "hounds placed along a line of chase," from Middle French relai "reserve pack of hounds or other animals" (13c.), from Old French relaier "to exchange tired animals for fresh," literally "leave behind," from re- "back" (see re-) + laier "leave, let." This is perhaps a variant of Old French laissier, from Latin laxare "slacken, undo" (see lax). But Watkins has it from Frankish *laibjan, from a Proto-Germanic causative form of PIE root *leip- "to stick, adhere." The etymological sense is "to leave (dogs) behind (in order to take fresh ones)." Of horses, 1650s. Electromagnetic sense first recorded 1860. As a type of foot-race, it is attested from 1898.
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