A dare is a challenge, often to do something silly or reckless. For instance, someone might say, "I dare you to run down the street naked." If you refuse, you might be called a chicken or otherwise shamed.

A "double-dog dare" just means that the dare is supposed to be harder to turn down than a regular dare. If you turn down a dare from somone, they may come back and say, "Oh yeah? Well I double-dog dare you!" Most kids find a double-dog dare impossible to turn down.

The movie "A Christmas Story" refers to the almost unheard of "triple dog dare" when one character dares another to stick his tongue on a frozen flagpole. You can guess what happened.