Google's Inbox adds new feature that disables notifications except for "high priority" email
The new high priority email feature could arrive via an OTA update or by a server-side update
You might recall Google's Inbox app. Originally offered by invitation only, the app helps organize your email inbox (hence its moniker) and bundles similar messages. This allows users to delete a ton of emails they don't want, with a single swipe. Emails can be snoozed and returned to your inbox when you are ready to read and/or reply to a specific message. The app is designed to work best with Gmail.
A new high priority feature for Inbox disables notifications except for high priority email
Screenshots show that the new feature will allow Inbox users to toggle on or off Notifications. If the setting is enabled, the user will be able to set the level required for a message to generate a notification to high priority, or lower. Hopefully, the new high priority feature will reach your handset shortly.
Download and install Inbox on your device by clicking on the appropriate link (Android|iOS).
source: AndroidPolice
Things that are NOT allowed: