Skeuomorphism design is the fact of graphically representing an object in an user interface by copying its shape, material and functionalities. For giving more reality to the object, shadows are also often used.
The old Apple newsstand bookshelf - before IOS7 - is often given as a typical example of skeuomorphism.
Calculators on smartphones and computers are also a good example of skeuomorphism in design.
Skeuomorphism is often opposed to flat design.