early 15c., remainen, "be left after the removal or loss of a part, number, or quality; survive," from Anglo-French remayn-, Old French remain- (as inil remaint "it remains"), stressed stem of remanoir "to stay, dwell, remain; be left; hold out," from Latin remanere "to remain, to stay behind; be left behind; endure, abide, last" (source also of Old Spanish remaner, Italian rimanere), from re- "back" (see re-) + manere "to stay, remain" (from PIE root *men- (3) "to remain").
Also from early 15c. as "continue" in someone's charge or possession; continue in a certain place or condition." From early 15c. in mathematics. Related: Remained; remaining.
late 15c., "those left over or surviving," from Old French remain, back-formation (verbal noun) from remanoir, remaindre "to stay, dwell, remain, be left," or else formed in Middle English from remain (v.).
The more usual noun in English has been remainder (n.), also see remnant, except in remains "a survival, relic, remaining part of something" (c. 1500), especially "that which remains of a human body after life is gone, corpse," which sense is attested from c. 1700. As "literary work (especially if unpublished) left by an author" from 1650s.
A native word would be leavings. Old English had yþlafe "the leavings of the waves," a kenning for "shore," daroþa lāf "leavings of spears," a kenning for "survivors" (of a battle).