The Old French word but meant "end" — think of "butt" for a crude way to remember that! — and it was joined to a-, from the Latin ad- "near to." The result was abuter, which meant "to touch at an end." The word eventually became abouter, meaning "to join at the ends, or border on." The idea of abut suggesting a common boundary comes from the late Middle English, and today we use the word when anything touches something else.