In general, a wrapper class is any class which “wraps” or “encapsulates” the functionality of another class or component. These are useful by providing a level of abstraction from the implementation of the underlying class or component; for example, wrapper classes that wrap COM components can manage the process of invoking the COM component without bothering the calling code with it. They can also simplify the use of the underlying object by reducing the number interface points involved; frequently, this makes for more secure use of underlying components.
Just what it sounds like: a class that “wraps” the functionality of another class or API in a simpler or merely different API.
See: Adapter pattern, Facade pattern