Destruction and violence are awesome.
Destruction Is Cool is when destructive, violent, and generally aggressive acts, movements and scenes are represented and/or perceived as awe-inspiring and/or awesome. Grand battles, a Wave Motion Gun, Stuff Blowing Up, Incendiary Exponent... or simply a punch to the face, or even a Precision F-Strike (there's a reason this dialogue trope is named like a military procedure). They're worthy of respect. They're demonstrations of dynamism and power. Power to impose one's will to the world, power to protect. Of course, such power might be better demonstrated in construction, but somehow building and growing takes too much time, thought, planning, and effort for it to be enjoyable in narration, especially in visual media. You can't argue with the visual "impact" violence and destruction have. There might a biological justification in that apes (chimpanzees in particular) can and do enjoy quick, intense releases of violence and noise as a way of social self-promotion. It get to the point that if a chimp leader is unable to throw the daily tantrum as intensely and noisily as usual (say, because of sprained ankle or a cold or something equally silly), the other chimps think he's gone soft, and it won't be long 'till he's toppled. Contrast with Construction Is Awesome. See the related Evil Is Cool, which this trope may lead to, but evil can create as well. As it is nigh-universal, examples should be kept to subversions, lampshades and other surprises.