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The wrapper acts as an interface between its caller and the wrapped code. This may be done for compatibility, e.g. if the wrapped code is in a different programming language or uses different calling conventions, for security, e.g. to prevent the calling program from executing certain functions, to provide a level of emulation, e.g. a DirectX API which uses OpenGL to render its graphics.
The implication is that the wrapped code can only be accessed via the wrapper.
In packaging, a wrapper is a flat sheet made out of paper, cellophane or plastic which is folded or vacuum sealed to enclose an object and protect it from wear and tear.