Below are the steps to start the SharePoint 2013 User Profile Synchronization Service.
Local Administrator
Ensure the service account is a member of the local machine Administrators group.
Grant “Replicating Directory Changes” permission
Using the Active Directory Users and Computers manager, grant “Replicating Directory Changes” permission to the service account (SP_Farm).
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Restart the SharePoint Timer Service
Start the SharePoint Server Synchronization Service
The service can take several minutes to start.
I followed under given URL which saved lot of my time. It is a very detailed article which also provided information about the user registration on Active Directory too. Hope this might help someone else to same few minutes.
http://www.windowstechupdates.com/user-profile-synchronization-service-not-starting-in-sharepoint-2013/