People running Windows Insider Preview release 14.14312 are getting the taste of a future in which Microsoft Edge pushes website notifications to your desktop. These notifications, which are meant to keep "users informed of new messages or alerts and allow sites to improve user engagement," are basically small windows that will pop up and let you know if something's changed on a website.
The notion of website notifications comes from the W3C, which outlined a framework for allowing websites some way of updating readers in real time (sort of like push technology in the 1990s).
The Windows blog offers a breakdown of how this notification framework is implemented in Edge, and notes that users will have to grant permission to a website before it can push notifications, and it's easy to manage or revoke permissions via Edge's Advanced Settings menu. Users can also disable notifications by right-clicking on the notification request or on a notification.
The Alerts feature will be available to all Microsoft Edge users this summer with the Windows 10 Anniversary Update.