Final answer:
Charles Darwin's first critical discovery was the variation of finches on the Galápagos Islands, which played a key role in developing his theory of evolution by natural selection.
Step-by-step explanation:
Charles Darwin made his first important discovery in the Galápagos Islands during his voyage on the HMS Beagle. From 1831 to 1836, Darwin traveled around the world, and it was on the Galápagos that he observed distinct differences among species that were otherwise similar. Notably, he found several species of finches, with each species having a unique beak shape that was adapted to its specific diet and environment. These observations of the Galápagos finches were critical in the development of his theory of evolution by natural selection.