Microsoft introduced a feature called Clutter, that will route emails that don't seem important to the user to another folder called Other. This was a good approach to help users focus on emails that would be important to them, and they can check the Other folder later on, however, users needed to visit another folder in order to see emails. That's why Microsoft introduced Focused/Other filters.

Now in Office 365, emails will have 2 filter tabs, Focused and Other. Important emails are going to appear in the Focused tab, and other emails will appear the other tab clearly. Now a lot of questions might come up when using these features, so let's review some of them: 

• How can a user control what emails appear in other and what emails appear in focused tab? 

There are algorithms that teach the application what emails are good enough to appear in the Focused tab, so once a user moves an email from the Other tab to the Focused tab, Outlook will know that this email source is important for the user, and it'll make sure to make upcoming emails from this source appear in the Focused tab.

• Can a user disable this whole functionality in his Outlook application?

Yes, you can do so by selecting the filter dropdown beside the tabs, and unchecking the option to "Show Focused Inbox", as shown in the image below: 

Now let's have a look at this scenario, let's say you're working on a project inside SharePoint online, and one of your colleagues mentions you in the newsfeed inside that project portal, like the following image: 

You're going to receive an email from: no-reply@sharepointonline.com,  But .. That email is going to appear only under the Other tab, and here's the catch, you won't receive notifications for emails that appear under the Other tab. By notifications I mean, you won't get notified when you're working in Office 365 that you received a new email: 

Remember that the newsfeed web part only sends emails when you're mentioned. 

So how do you solve this? You can't just ask each employee to disable the Focused functionality. You have 2 options in this case, either tell Exchange Online to route all emails from no-reply@sharepointonline.com to the Focused tab, or you can just disable the Focused inbox functionality on the tenancy level. Here's how we can do that: 

Go to your Office 365 Exchange admin center, and from the left navigation, click "mail flow". Click the + sign to add a new rule: 

A new window will appear, that looks like this: 

Give the rule a name, let's say: "Other to Focused Emails Routing", then choose "The recipient address includes…" and click "Enter words…" and add the address you want to appear under Focused tab for all users, in this case no-reply@sharepointonline.com, then click the + sign and hit OK. 

Then go all the way down and click "More options…":  

In the "Do the following…" dropdown list, choose: Modify the message properties > set  a message header

Set the header to: X-MS-Exchange-Organization-BypassFocusedInbox  and the value to true. So the final result should be: 

Click save, and that's it. You can wait for a couple of minutes, and then test it. Upcoming emails will be delivered to the Focused tab, and you will receive notifications.

The other option would be to disable the Focused inbox functionality for all users in the tenancy, which leaves you with PowerShell. Once you connect to Exchange Online using PowerShell, you can run the following 2 commands: 

Get-OrganizationConfig

Set-OrganizationConfig -FocusedInboxOn $false

I prefer doing the first approach, and just routing the important emails to users' Focused tab, and give them the freedom to have it if they need.