Information on the Focused Inbox in Outlook 2016 for Windows or Mac desktop is at "Focused Inbox in Outlook desktop"
The Focused Inbox was first introduced in the Outlook app for smartphones and began rolling out to Outlook on the web in October 2016. It will be coming to Outlook 2016 subscriptions in the coming months. The Focused Inbox is a filter, not a folder, and the goal is to have less important mail shown under the Other tab and important mail under the Focused tab.
When the Focused Inbox filter is enabled, you'll see two tabs at the top of the message list, named Focused and Other. If there are new items in tab that is not selected, the first line of the message list will tell you have many new messages there are and include some of the senders names.
As you can see in this screenshot, the selected tab (Focused) is very lightly bolded.
If Outlook filters messages wrong, either right-click on the message and choose Move to... Focused Inbox or use the Move to button in the bar. You can choose to move just the selected message or all messages from that sender or thread.
Turn off Focused Inbox in Outlook on the web
You can turn Focused Inbox off (or on) in Outlook on the web from the Inbox - click on the Filter menu and deselect Show Focused Inbox at the bottom of the menu.
Turn off Focused Inbox in Outlook desktop
Outlook desktop has a Focused button on the ribbon and in the menu to the right of the Focused/Other tabs that toggles Focused Inbox off and on.
For more information and additional screenshots, see
Outlook for iOS and Android
To use, click the Focused or Other tab at the top of the message list to switch between focused and other. At the the very top of the list you'll see the From name of new messages in the group you aren't viewing.
If you don't want to use it, you can turn the Focused Inbox off.
Turn off Focused Inbox on iOS devices
Click Settings at the bottom right. The Focused Inbox toggle is near the bottom of the Settings page. The change should take effect immediately.
Turn off Focused Inbox on Android
Click 3 dots on the right, then Settings.
Toggle Focused Inbox off. You'll need to close and restart the Outlook app for the change to apply.