Koopa hopping is a technique that (I think) can be applied for all characters. If it can be used by all characters, however, Bowser can do it much more easily or noticeably, hence why his Japanese name is used to describe it. Basically, coming off of your first jump, just before you hit the ground, you use forward B and then jump. If used correctly, you will immediately go into the second jump, and if you continue to perform it correctly, you will be able to use your second jump for as long as you want. It's a great way to get out of landing lag, especially for Bowser.
OK, I'm home right now, and I'll be able to Brawl anytime tonight or tomorrow. But Sunday, I'm gone again. If anyone wants to Brawl me, there ya go.
EDIT: So it's FORWARD B, NOT forward Aerial! No wonder I've been screwing it up >_<.