To wrap up is to finish something off — or to dress warmly. Two senses, and only one involves paper.
The finishing sense is used about meetings, filming and negotiations, so wrapping up a discussion means bringing it to a close, and in film the wrap is the moment shooting ends. The dressing sense is British and warm, since being told to wrap up warm before going out is a piece of maternal advice everybody recognises. The literal sense of wrapping a present sits underneath both.
Practised in Phrasal Verbs, A Man Called Ove
First appears in chapter 22 of A Man Called Ove.
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