When you challenge or provoke someone to try something risky, it's a dare. If you accept a dare, you're probably trying to prove how brave you are.
When you challenge your friend to a dare, you dare him. You might, for example, dare your brother to jump off the garage into a pile of leaves. Another way to dare is to actually be brave: "I admire her so much, because she dares to stand up to bullies." The Old English root of dare is durran, "to brave danger, venture, or presume." If you say, "How dare you?" you're expressing outrage or indignation.