Sole means not shared with others. If it's your sole responsibility to make the chocolate cake for a party, it's all on you.
Sole comes from the Latin solus, meaning "alone," and it can describe being the only person involved in something, like being the sole member of the Special People Club. As a noun, your sole is the bottom of your foot. If you order sole in a restaurant, you'll get a flat fish that looks like the bottom of your shoe. Although they sound alike, if you order the soul, the waitperson might send you to a church down the street.