The word thumb comes, via Old English, from the Proto-Germanic word tûmon meaning "thick" or "stout". So a thumb was called "tumon" because it was the thickest, stoutest finger. This, over the centuries, evolved into the Modern English word thumb.
As it turns out, "tumon" is related to the Latin word "tumere" which means "to swell", from which we get the English word tumor, meaning a swelling caused by an uncontrolled growth of cells.
(from the OED)