late 14c., "place for washing;" mid-15c., "act of washing," a contraction (compare launder) of Middle English lavendrie (late 13c.), from Old French lavanderie "wash-house," from Vulgar Latin *lavandaria "things to be washed," plural of lavandarium, from Latin lavare "to wash" (from PIE root *leue- "to wash"). English meaning "articles that need to be or have been laundered" is from 1916. As a verb, from 1880. Laundry list in figurative sense is from 1958.
c. 1300, rinsen, rincen, "subject to light washing; wash with water only" (originally in liturgy; from mid-13c. in surname Rinsfet), from Old French reincier (transitive) "to wash, cleanse" (12c., Modern French rincer), probably a dissimilation of recincier, from Vulgar Latin *recentiare "to make fresh, to wash, cleanse with water," from Late Latin recentare "to make fresh," from Latin recens "new, fresh" (see recent). OED says any similarity in form and sense with Old Norse hreinsa is "prob[ably] accidental."
In general use, of bowls, cups, etc., c. 1400; the meaning "wash (laundry) a second time to remove remaining impurities, soap, etc. that may have been left" is by c. 1500. Related: Rinsed; rinsing.