From Latin 'implicāre' (to fold in) — folding meaning inside a statement rather than displaying it; kin to 'implicit' and 'implicate.'
To suggest or indicate something without stating it directly; to involve as a necessary consequence.
From Old French 'emplier' (to enfold, to involve, to wrap up), from Latin 'implicāre' (to fold in, to entangle, to involve, to enfold), composed of 'in-' (in, into) + 'plicāre' (to fold, to plait, to bend), from PIE *pleḱ- (to plait, to fold, to weave into). The literal metaphor is compelling: an implied meaning is one folded inside the statement, not laid out on the surface. 'Imply' is the vernacular doublet of the learned 'implicate' — they come
The distinction between 'imply' and 'infer' — one of English's most policed usage boundaries — maps onto a sender/receiver split: the speaker implies (folds meaning in), the listener infers (carries meaning away). Despite generations of grammarians insisting on the distinction, 'infer' has been used to mean 'imply' since the sixteenth century.