Your shoulders are at the very top of your arms, where they meet your neck. When you shrug your shoulders, you lift them to convey indifference or the fact that you don't know the answer.
Human shoulders are versatile ball-and-socket joints that are flexible but sturdy enough to allow for lifting heavy objects. Another kind of shoulder is the strip at the side of a road where you can pull your car over in an emergency. This word is also used as a verb, for literally or figuratively carrying heavy burdens: "You shoulder so much responsibility at work — they should give you a raise!" Give someone "the cold shoulder," and you're deliberately being unfriendly to them.