What I did was that I drank a bottle of beer (no beer was hurt in this clip) and nearly filled the bottle with water. I then gripped the bottle tightly with my left hand and used "Batangson Naryeo Chigi" or a strike with my opened hand on the opening of the bottle. When done with sufficient strength you actually push the air inside the bottle downwards usually resulting in the bottom of the bottle to fall cleanly off (this time almost the whole bottle broke instead). Kids do not try this at home:-)
Martial applications or relevance? Almost zero. It only demonstrates that the "breaker" (me) has strong gripping strength and that he can focus a lot of power on a small surface resulting in the break. My guess is that any traditional trained Taekwondoin blue belt and above should be able to replicate this with no problems at all. Even untrained adults should be able to do this as long as they can strike hard with their opened palm and possess enough gripping strength.