Synchronization Services Manager use for verify SharePoint User Profile Synchronization is work but some people may get this error when start this application.
Unable to Connect to the Synchronization Service
Some possible reasons are:
1.The service is not started.
2.Your account is not a member of a require security group.
1.make sure that 2 FIM Services in Synchronization Server is running.
2.make sure that your current user is in FIMSyncOperators group. if not add your user account then log off and log on.
After that, you should be able to access this application.