Natural selection.
A trait such as beak size that caused its possessor to have a reproductive advantage would be favored by the process called "natural selection", and over time descendants of the ancestral Galapagos finch evolved into 14 species with different beaks.
The 14 "Darwin's finches" on the Galapagos Islands all evolved from a common ancestor by adapting their beaks to different food sources.
Birds 1, 3, 4, 5, 6, and 10 are classified as tree finches (bird 10 is a woodpecker finch). Birds 7, 8, 11, 12, 13, and 14 are known as ground finches, bird 2 is a warbler finch, and bird 9 is a Cocos finch (a finch living on Cocos Island).