Answer:
The principle influence was Darwin reading Principles of Geology by Charles Lyell - he was given a copy by Robert Fitzroy (the captain of the Beagle) at the start of the Beagle's voyage around the world.
The main theme of Principles of Geology is uniformtarianism. This is the theory that the world was shaped by the gradual affect of observable processes. For example, a river valley is explained by the river gradually wearing through the rocks.
It is the idea of uniformtarianism that Darwin applied so successfully to explain how new species could evolve.