A layer placed around something to hold or adapt it. It adds handling without changing the contents.
Middle English wrappen (of uncertain further origin, attested from c. 1300) plus the Old English agent suffix -ere; a wrapper is literally "the thing that wraps" — whatever encloses, without altering, what it holds.
Handling added entirely from the outside, in a layer that touches nothing within — whatever gets wrapped keeps its own contents exactly as they were before. Only the approach reaching it from outside changes; the thing being reached stays itself.