You arrived here because you cannot open Mail, Safari or calculator app and you do not know how to fix your iPhone.

Without much introduction, here is the fix:

1. Uninstall AppSync then respring your device;
2. Open MobileTerminal (install it first) and navigate to /var/mobile/Library/Caches;
3. Delete the following file:
com.apple.mobile.installation.plist
4. Reboot your iPhone
5. Your applications should start now without any problems and you can install back AppSync if you want.

NOTE: after reboot, you will not find your AppStore apps on the device but do not worry, they will reappear shortly.