What do I do when I get a "sync session failed to start" message when syncing iPhone to itunes? The context is that I'm restoring my wife's new replacement iPhone from a backup. It already did the first sync, where it gets all the settings and whatnot, but not the apps.  Tried the second sync, where it normally transfers the apps, but I'm getting the error message.
On your iPhone, force close all the Apps in the multitask window. Depending on your version of iOS, you do the following:

On iOS 7 and before:


From the Home screen, click the Home button twice. 
Tap and hold on the app. 
When it starts to jiggle, tap the X to close it.
Repeat until all the apps have been closed.


On iOS 8:


From the Home screen, click the Home button twice. 
Swipe the application preview window upwards to close the app. (you can close multiple apps at once)
Repeat until all the apps have been closed.


Now do a Soft reset of your iPhone:
Hold both Home and Sleep button for around 10secs until you see the Apple logo then release. After it returns to Home screen, connect to sync and see if this resolves the issue.

Source: https://discussions.apple.com/message/18381241#18381241