Why did Darwin formulate his theory of evolution just after his visit to the Galápagos islands? Why were they so special from an evolutionary point of view?
Charles Darwin formulated his theory after travelling the world aboard the Beagle, here's the route. He found the Galapagos Islands particularly inspiring,
'The natural history of this archipelago is very remarkable: it seems to be a little world within itself.'
This is a more detailed account of his relationship with the Galapagos islands, and there is also a book called "Voyage of The Beagle" (I think it is available as a free kindle download) which is basically his diary.
A big part of the reason it is so famous is because of "Darwin's Finches," which are 12 species of finch on the island that have all evolved to specific niches. This is one of the classic examples of evolution. Darwin noted the differences between the birds, thinking they were of different families, but it was later discovered they were all finches and the differences had evolved because of factors like the food they eat (seed eaters had fatter beaks.. etc).
The Galapagos islands offer opportunities to study evolution and adaptation because the islands are distant from the mainland, have differences between the islands, and migration between the islands is difficult. Studies like this one (which I happened to be reading at the time of the question being asked whilst writing a manuscript) are an example of how cool a place it is!
Galápagos islands are one of few islands with a unique fauna and flora. This can only happen when the distance to other land is great enough, and when the island exists long enough that flora and fauna could grow (volcano islands are sterile for a long time).
Now Galápagos is even more unique because it is comprised of several islands that are distant enough that some animals cannot cross the distance like small birds. That leads to a unique fauna and flora that also differs between islands, so you can see differences just by visiting the next island. This made it practically a museum of evolution.