iOS 7
It has to do with app cacheing from the App Store. Have you downloaded ALOT of apps with your Apple ID? Even if you delete them from your springboard, they can still appear in Apple's app chaches on your device, and when this gets too high (too much for the RAM to handle), it starts passing the cache tasking to the SSD, which can cause issues and glitches such as this. I suggest going into the App Store from iTunes (on a computer), Purchases, and manually disabling ("deleting") apps that you no longer use. After that, sign out and then back in to your Apple ID and iCloud accounts and restart your phone. If the problem persists, a full restore as NEW (do NOT restore from backup) is more than likely the best course of action.
Reboot the device
This has been a side effect of jailbreaking since the beginning of time. It's usually caused by a tweak. There was a tweak I used to use back in the day (this hasn't happened to me in a couple years now...knock on wood) called iRetiner GUI that has a feature which fixes the white icon issue. Not sure if it works on iOS 7 yet though. But this is what I used all the time and it worked wonders for me.
Also, I believe SBSettings also sometimes fixed this problem if you used the "fix user permission" button or whatever it's called.
Edit: I think there were a couple other tweaks which tried to fix this too. You might be able to run RM Cache, fsWipeCache, or iWipe Cache to fix this. Not sure if any of these have been updated for iOS 7.