Are you trying to update the apps on your device ahead of the release of iOS 7 and having trouble connecting to the App Store? The chances are that you may need to accept the new App Store terms and conditions.
The App Store should prompt you to accept the new terms and conditions when you either try to update an app, or when you download a new app for the first time. It may not grab you straight away, but when it does, you should be seeing the screen shown up top. Accept, and you're good to go!