To complete, finish, or conclude something, often with final details or summary.
From the literal act of wrapping packages or gifts, first recorded in the 1920s. The figurative sense of 'completing' emerged in the 1940s, suggesting the neat, tidy conclusion that comes with properly wrapping something.
The phrase implies more than just ending - it suggests bringing something to a neat, organized conclusion with all loose ends tied up. It's the verbal equivalent of putting a bow on a present, which explains why we feel satisfied when we 'wrap up' a project successfully.
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