Well, a meteor attack intentionally and only sends your opponent downward at fast speeds (hence the name "meteor"). PB is right - it's not necessarily a strong attack, but the point is that it is difficult to recover from. At higher damage percentages, it's almost impossible because you're going to fly away quicker.
A really good Smash player can actually jump out, perform a Meteor, and then recover back to the platform. They'll also guard the edge and do their meteors with short hops. Again, the demo of Mario slamming down Bowser is a good example. Bowser flies straight down. Kirby's down-B tends to actually send characters upward and/or just cause some damage - it doesn't actually cause a directional influence on where you get hit.
Meanwhile, Falco's jumping down-A smash is that spinning "needle kick," and if you guard the edge with it, chances are you're going to get the KO. Short hopping this meteor is particularly devastating because you'll normally just be out of right of an opponent's third jump attack, and be given priority when you hit them during your descent.
I guess you can recover from them, or maybe just the computer AI gets to cheat around it. The point is that a meteor is a devastating attack when you're pretty much over 50% - the chance of you recovering from one are slim.
Down-B attacks typically aren't meteors to my knowledge. I'm sure if you went to Gamefaqs they'll have guides for every character detailing exactly what their meteors are. Again, most of the time it's a down-A smash in midair.