App Store Down
One of the most problems is that the App Store is down or is saying that it's down on your iPhone.
Usually the App Store is down because there's a problem with Apple's servers. It usually only happens a few times a year, but it always seems to happen at the worst times.
However, it's always a good idea to check your internet connection on your iPhone and make sure that the problem isn't on your end before you blame Apple. Otherwise, you'll just have to wait it out and hope Apple fixes the problem soon.