late 14c., implien, emplien "to enfold, enwrap, entangle" (the classical Latin sense), from Old French emplier, from Latin implicare "involve, enfold, entangle," from assimilated form of in- "into, in, on, upon" (from PIE root *en "in") + plicare "to fold" (from PIE root *plek- "to plait").
Meaning "to involve something unstated as a logical consequence" first recorded c. 1400; that of "to hint at" is from 1580s. Related: Implied; implying. The distinction between imply and infer is in "What do you imply by that remark?" but, "What am I to infer from that remark?" Or, as Century Dictionary puts it, "An action implies ability or preparation, but involves consequences."