Human beings abstract things on two dimensions: part-of and kind-of. We say that a Ford Taurus is-a-kind-of-a Car, and that a Ford Taurus has parts such as Engine, Tire, etc. The part-of hierarchy has been a first class part of software since the ADT style became relevant, but programmers have had to whip up their own customized techniques for simulating kind-of (usually in an ad hoc manner). Inheritance changes that; it adds 'the other' major dimension of decomposition.
An example of 'kind-of decomposition', consider the genus/species biology charts. Knowing the internal parts of various fauna and flora is important for certain applications, but knowing the groupings (kinds, categories) is equally important.
