One interesting way to undestand the specificity of evolution is, ironically, to treat it as a non-biological phenomenon, as much as a biological one. After all, if we stick to the strict definition of evolution as 'descent with modification' (the passing of traits from one generation to the next), it becomes clear that organisms are not the only 'entities' that can undergo evolution. Understood in the strict and/or broad sense above, the idea of evolution is, as it were, 'substrate-independant'. Darwin himself implicitly recognized this when he drew attention to what he called the 'striking homologies' between the evolution of species and the evolution - although he did not call it that - of language:

"The formation of divergent languages and of distinct species, and the proofs that both have been developed through a gradual process, are curiously the same... We find in distinct languages striking homologies due to community of descent and analogies due to a similar process of formation. [For example,] the manner in which certain letters or sounds change when others change is very like correlated growth. ... Languages, like organic beings, can be classed either naturally according to descent, or artificially by other characters. Dominant languages and dialects spread widely and lead to the gradual extinction of other tongues. A language, like a species, when once extinct, never... reappears. The same language never has two birthplaces. Distinct languages may be crossed or blended together." (Darwin, The Descent of Man).

Languages, like organic species, go extinct and die; they 'speciate' (or 'dialectize') through geographic isolation; and grammatical categories reflect the 'fitness' of a language with respect to the things it tries to get across (I won't substantiate this claim too much, other than by pointing to this paper which fills it out more). But language is only one example. One can also look at technology as another: consider the mobile/cell phone industry. One can think of cellphone models as populations of species distributed among environments, each vying for survival (based on features, usefulness, aesthetic criteria, economic considerations, advertising, etc). Any in any case, the comparison between language and technology shouldn't be so far fetched to the degree that language is indeed nothing other than a natural technology in it's own right (also see this paper which directly applies evolutionary principles to cellphone evolution).

So far we've talked only of 'natural' systems. But evolutionary principles can also be applied to artificial ones as well, as has been done in the case of both (1) architecture and (2) circuit-design. In the case of architecture, we can program computers to generate varying 'species' of architectural designs in order to meet certain criteria (a column must be able to bear a certain load, the building must have enough windows, etc), while eliminating those generated designs that do not pass the test of - in this case - artificial selection (read more on using genetic algorithms to design things here). In circuit-deisgn, the idea is the same: get a computer to simulate a whole series of circuits (the stuff your CPUs run on) in order to come up with the most efficient design so that your computer can process things fast and with minimal resources (the 'fittest' circuit design).

These are all just small examples from disparate fields, but I hope they begin to fill out a picture of how to understand evolution as not just an organic process, but an inorganic one as well. There are caveats to all of this of course, but perhaps they come through in any discussion that follows. The geneticist Theodosius Dobzhansky once wrote that "nothing in biology makes sense except in the light of evolution"- and while he was undoubtedly right about this, perhaps he was being too modest; the same ought to be said of a great deal else in the world as well - that ultimately, we need to look at the world sub specie evolutionis.