That's the sound you make when you're falling to your death after dropping your sandwich on the keyboard, causing you to dismount while 600 feet in the air.
(That's also the sound you make when playing on beta, and Blizzard makes every 17 feet have a flying deadzone that randomly dismounts you)
Anyway, Aieeeeee! will save you the hassle of falling-death repair bills. When it figures out that you're about to paint the pavement a nice shade of pinkish-red, it'll go ahead and take all your durability-affected gear off, so that you don't get any messy bloodstains on it. I mean, it took you so long to farm the mats for that Mooncloth Robe, it'd be a real shame to stain it and have to take it to the dry cleaners AGAIN. Those Mooncloth tailors really need to figure out how to make a machine-washable robe.
Aieeeeee! will also go ahead and put your gear back on when you rez. Or if you survive. But it's kinda disappointed if that happens, because then it can't really do its job.
Do Aieeeeee! a favor today. Go throw yourself off a cliff. It'll thank you for it, and you'll thank it.
Short Version: Aieeeeee! saves you gold. Any time you're going to fall to your death, Aieeeeee! will unequip your gear for you. If you don't die, or you rez, Aieeeeee! will put it back on.
This may be useful in Northrend.