To stamp out something is to end it. You might have learned at summer camp how to stamp out a fire, or to put it out quickly by stepping on it.
To stamp out a campfire is to extinguish it, or put it out; to stamp out something figuratively means the same thing. For example, a teacher might try to stamp out her students' collective anger about a difficult pop quiz, or a dictator might stamp out any hint of revolution in his country. This common verb was first used in the mid-1850's, originally in the sense of "put out a fire."