1. Short for "wrapper":
This is the most common usage and applies to things like food wrappers, gift wrap, etc. It's simply a shortened form of the word "wrapper."
2. From "to wrap up":
This phrase means "to finish" or "to conclude." "A wrap" could be used as a short form of this, meaning "it's finished" or "that's all."
3. "Wrap" as a noun:
In some contexts, "wrap" can be a noun itself, referring to a covering, an enclosure, or a container. This is less common but still possible.
4. Slang for "a wrap party":
This refers to a party celebrating the completion of a project, film, etc. "A wrap" could be used to mean "the end of the project" or "the party is happening."
It's hard to say definitively which origin is the "true" one, as the expression has evolved over time. The meaning is usually clear based on the context.