This problem is not uncommon but the source of it can be any number of things. Perform steps below in progression and as required to resolve the issue:
1. Problem with Apple ID. Sign out of your iTunes account via Settings/Store/Apple ID/Sign out. Now sign back into your Apple ID and view your account via Settings/Store/Apple ID/View Apple ID. Now verify your payment method on the account (credit card or gift card) and make sure neither is expired, invalid, or exhausted in the case of a gift card. Correct as required. Now check to see if waiting app is now loading/installing.
2. Sign into your iTunes account from within iTunes on your PC. Do NOT connect your iPad at this time. Verify that no pending downloads are present in iTunes whether it be an app, a podcast, a song, a movie, or TV show. Resume and complete any orphaned downloads you may find. Now check to see if waiting app is now loading/installing.
3. From within iTunes download the app that is waiting on the iPad. Confirm it completes normally. Change iTunes sync option to manual. Attach iPad. Perform manual sync of problem app from PC to iPad.