Authoritative Active Directory (AD) restores are necessary when you wish to restore not just the target machine, but all other machines in the domain with AD. The authoritative restore process returns a designated object or container of objects to its state at the time of the AD backup. For example, an authoritative restore might be required if you accidentally delete an organizational unit (OU) containing a large number of users. The default nonauthoritative restore will not recover deleted OU because the restored domain controller will match the current status of its replication partners after the recovery, and the partners will have OUs deleted. When you mark the AD restore as Authoritative, the AD replication process will propagate the recovered OUs to other Domain Controllers in the domain.
Making the restored AD Domain Controller authoritative as described above does not automatically propagate SYSVOL state to other controllers in the domain. Instructions on that process are available from Microsoft here.