I found the solution! This happened to me, too, after restoring from iTunes backup: most of my apps were stuck in a "dark" status and if I clicked on one then it would change to a "waiting" status. I did a lot of tapping and restarting and Google searching, and here's what fixed it for me:
Open iTunes, go to the Apps in your LIBRARY (in the top left toolbar of iTunes) -- not on your iPhone/iPad/iPod -- make sure you're in the "icons" view not the "list" view, and then up top (in iTunes v12 anyway) click the filter above the icons that says "Updates" (to show only apps in your iTunes library that have updates available), then in the bottom right click the [Update All] button. You can also update individual apps by right-clicking on them, or you can drag a box around a group of apps and then right-click.
Once all your apps in your iTunes library are updated, then [Sync] your iPhone/iPad/iPod and the sync process will install all the gray and "waiting" apps to your device.