early 15c., redemen, "buy back, ransom, recover by purchase," also in a theological sense, "deliver from sin and spiritual death," from Old French redimer "buy back" and directly from Latin redimere "to redeem, buy back," from red- "back" (see re-) + emere "to take, buy, gain, procure" (from PIE root *em- "to take, distribute").
In Middle English, Latin redimere sometimes was translated as againbuy. The general sense of "rescue, deliver, save" is from late 15c. The meaning "make amends for" is from 1520s. Sense of "make good, perform, fulfill" (a promise, obligation, etc.) is from 1840. The commercial sense of "receive back by paying the obligation" is by 1889. The sense of "save (time) from being lost" (Tindale, Shakespeare, Young, Cowper, Eliot) is after Ephesians v.16, Colossians iv.5. Related: Redeemed; redeeming; redempt (obsolete).