Go to Settings>General>Date and Time>Set Automatically>On. Make sure that is set that way and make sure that your time zone is correct. If everything is correct, change the date and time to anything else and then try to download an app. If you get an error message, go back and set it to automatic again and then try downloading again.
You can try restarting your router - even though everything else is connecting OK - it can still help. Unplug it from power for about 30 seconds and then plug it in again.
If those suggestions dont help - in this order ..... close the apps store app, sign out of your ID, reboot your iPad, sign in again and then try to download again.
To close apps, Double tap the home button and you will see apps lined up going left to right across the screen. Swipe to get to the App Store app then swipe "up" on the app preview thumbnail to close it.
Go to Settings>iTunes & App Store>Tap your ID and sign out,
Now reboot the iPad. Reboot the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider if it appears on the screen - let go of the buttons. Let the iPad start up.
Go go back to Settings>iTunes & App Store>Apple ID>Sign in then try to download an app again.