What does iTunes do while it's "Verifying iPod, iPad, iPhone"? What does iTunes do while it's "Verifying iPod, iPad, iPhone" 

I see this most often after an abruptl disconnect and plug it back in but also sometimes when doing a second sync immediately after the last sync completes.

Does it fix any errors that have occurred on the device?
Your computer iTunes is waiting for the iPhone to "fix itself" and clean up from the interrupted sync.

The mobile iTunes database (and I'm sure several others) will need to be rebuilt to clean up after an interrupted sync. You can see/test this by disconnecting your iOS device in the middle of podcast or music syncing. If you then immediately start up iTunes for iOS - you will get an Updating LIbrary screen while it itdbprepserver does its work. You'll get a "verifying message" until these post-sync and interrupted-sync cleanup activities finish. Once iTunes on the desktop has "verified" the phone is ready to start another sync, it commences with the normal backup and sync activities. My timing shows the interrupted recovery to take twice the time of a normal sync completion but usually less than a minute either way.