late 14c., "envelop, surround; make cloudy or obscure," from Old French involver and directly from Latin involvere "envelop, surround, overwhelm," literally "roll into," from in- "in" (from PIE root *en "in") + volvere "to roll," from PIE root *wel- (3) "to turn, revolve." Mid-15c. as "concern oneself." Sense of "take in, include" first recorded c. 1600. Related: Involved; Involving.
Obscurest night involved the sky,
The Atlantic billows roared,
[Cowper, "The Castaway"]
c. 1400, in figurative sense of "to involve in difficulties," from mire (n.). Literal sense of "to plunge or fix in mire, sink or stall in mud" is from 1550s; that of "to cover in mud or filth" is from c. 1500. Related: Mired; miring.
Imply, which is the same word, retains more of the original sense. Sense of "hire, engage" first recorded in English 1580s, from meaning "involve in a particular purpose," which arose in Late Latin. Related: Employed; employing; employable.