a message or word sent via someone else; a verbal message or instruction (often expressed with the verb 言付ける — to give/send a message).
お母さんに『遅くなる』とだけ言付けて出かけた。
I left after only telling my mother, 'I'll be late.'
受付に言付けを残して、先に会議室へ入った。
I left a message at reception and went into the meeting room first.
彼は上司に言付けを頼まれ、伝言を届けた。
He was asked to deliver a message by his boss, and he conveyed it.
archaic meaning: an excuse or pretext; this usage is somewhat old-fashioned.
言付けを理由に家を出たが、本当は友人に会いに行った。
He left home using a pretext, but in fact he went to see a friend.