1. Literally, to extinguish a spark or fire by stamping on it with one's feet. A noun or pronoun can be used between "stamp" and "out." We quickly stamped out the fire so that it wouldn't be seen in the night sky. An ember popped out of the fireplace and onto the rug, so I stamped it out before it set the place alight.

2. By extension, to destroy, extinguish, or kill someone or something. A noun or pronoun can be used between "stamp" and "out." Scientists from around the world are joining together in a bid to stamp out the devastating disease. The dictator vowed to stamp the rebels out once and for all.