late 14c., relaxen, "to make (something) less compact or dense" (transitive), originally especially in medicine, of muscles, etc., from Old French relaschier "set free; soften; reduce" (14c.) and directly from Latin relaxare "relax, loosen, open, stretch out, widen again; make loose," from re- "back" (see re-) + laxare "loosen," from laxus "loose" (from PIE root *sleg- "be slack, be languid"). A doublet of release.
Meaning "decrease tension" is from early 15c. From 1660s as "to make less severe or rigorous." Intransitive sense of "become loose or languid" is by 1762; that of "become less tense" is recorded from 1935. Of persons, "to become less formal," by 1837. Related: Relaxed; relaxing. As a noun, "relaxation, an act of relaxing," from 17c.