Biogeography is simply the study of the locations of different species through space. Biogeography reveals that species that appear to be closely related tend to be geographically close as well, as though groups of species had a common origin at a particular geographic location and radiated out from there.
Charles Darwin carefully studied the biogeographical patterns of existing species. Darwin was especially interested in the study of species on islands, and he observed that they seemed to be most closely related to species found on the nearest mainland. Darwin was interested in what, if anything, these biogeographical patterns revealed about evolutionary history.
In developing his ideas, Darwin focused on finches that lived on the Galapagos Islands, an archipelago in the Pacific Ocean off South America. Several species of finches live on the Galapagos, each species inhabiting a different island. The species seemed quite similar to one another and to a species on the mainland, leading Darwin to hypothesize that the different species of Galapagos finches were descended from individuals in the mainland species that had reached the islands sometime in the past. Because conditions on the islands differed from conditions on the mainland, the selective pressures acting on the finches also differed, resulting in new traits being favored in the new environment.
As a result of the different evolutionary tracks between the mainland finches and island finches, the gradual changes accumulated to the point where the island finches were different enough from the mainland finches to be considered a new species.
This process occurred on the various Galapagos Islands, which are far enough apart that travel among them by finches is uncommon. After those rare events when finches did make it to a new island — perhaps as a result of being blown there by a storm — they evolved separately from the population on the island from which they came, in response to whatever novel environmental factors were present in their new home.
When Darwin proposed that the Galapagos Islands had become inhabited by so many different but apparently related species of finches through the process of evolution, he had only his observations of existing variation to rely on. Today's scientists, by analyzing DNA, have confirmed these relationships, and detailed studies support Darwin's hypotheses about the existence of different selective pressures on different islands.