It's not piracy per se
It's not piracy per se that makes AB so popular, but there some are similar effects between piracy and the AB model -
1) It's cheap
Piracy is generally free, but even buying the AB app is pocket change.
2) It's so darn easy to get a hold of
Piracy is sometimes that much easier (and quicker) to get hold of something than buying it thru proper channels. AB (altho this holds true for all mobile apps) is just as easy (if not easier) to get from the "proper" channel than to pirate it - fire up your phones app store, a few clicks, enter your pass, fire the thing up.
If music/video was cheap enough that ppl thought "meh, what's £x? May as well get it" they'd get less profit per item, but would likely increase total sales substantially (compare 'berry app prices and sales with Apple app for example - who the hell pays £5 for a phone app?!)
Try before you buy would likely help too - taster apps with a few levels to get you into the game go a long way to giving ppl a reason to buy your app.