The Focused Inbox feature is rolling out across Office 365 right now. Here's how the new feature works and how it replaces the old and sometimes much-maligned Clutter feature. In effect, we swap one way of separating the Inbox into important/unimportant messages for another. https://www.petri.com/focused-inbox-office-365
Neither Clutter nor Focused Inbox are on-premises features. Focused Inbox is being provided to users who have cloud mailboxes on Exchange Online as that's where the processing to separate inbound messages into the two views is performed.