How do the finches of The Galapagos observed by Charles Darwin prove the theory of evolution?

Birds in the Galapagos had widely varying beak shapes and coloration, reflecting their varied diets and resembled a variety of birds seen in various places in the world. Upon close anatomic study, they all had anatomic features unique to finches. It was apparent that a few finches arrived from South America and each subpopulation diversified based on the features most favorable to utilizing the various food sources.