The story as conventionally told (or at least as frequently remembered by many of us) is that Darwin, while traveling from island to island, noticed that the finches' beaks on each island were marvelously adapted for exploiting local resources — that on one island beaks were sturdy and short and good for cracking nuts, while on the next island beaks were perhaps long and thin and well suited for winkling food out of crevices — and it was this that set him to thinking that perhaps the birds had not been created this way, but had in a sense created themselves.
In fact, the birds had created themselves, but it wasn't Darwin who noticed it. At the time of the Beagle voyage, Darwin was fresh out of college and not yet an accomplished naturalist and so failed to see that the Galapagos birds were all of a type. It was his friend the ornithologist John Gould who realized that what Darwin had found was lots of finches with different talents. Unfortunately, in his inexperience Darwin had not noted which birds came from which islands. (He had made a similar error with tortoises.) It took years to sort the muddles out.