In order of increasing inconvenience:
- Quick fix: Restart your iPad. Press and hold the Sleep / Wake button until the red slider appears then slide it to shut off the iPad. Turn it back on again with the Sleep / Wake button.
- If that does not work, go to Settings > Store > Apple ID. Sign out by tapping your Apple ID then tap Sign Out. Sign in again. If an app still says "waiting" tap it to resume the download. Tap only one "waiting" icon.
- If that does not work tap and hold an icon (doesn't matter which) until they "shake". Choose an app still "waiting" and tap the red x to delete it, then try again.
- If that does not work, go to Settings > General > Reset > Reset All Settings. You will need to recreate your app and iOS preferences.
Also read this to ensure you do not have any pending iTunes Store downloads:
- If that does not work, restore your iPad as a last resort. You will need to restore it from your latest backup, or re-download all your previously downloaded content.
Agree with all of the above suggestions. One more that might work & has worked for me in the past is to update the app in itunes on your computer, then re-sync the iPad (assuming you've synced it with iTunes in the past). This pushed the new one to my ipad when I had a similar issue with a different app.