Maybe because App World is only available on a Blackberry?
Seriously, give us some details so we can help. What happens when you tap the app store icon? Does it shut instantly? Does it open and not connect (and if so, are you always attached to the same network when this happens)?
Your referring to the app store? (app world is for bb, lol) Have you tried a reset and/or a reboot of your phones? There have been a few issues going on with the app store the past few days. Some people have had to actually do a restore OR go to an Apple store to resolve the issue for now.