Twitter has released a new feature that allows the users to receive desktop notifications for direct messages on web.
According to the The Next Web, the notifications will show up on the top right side of the users screen. When the users click on it they will be taken to the DM interface.
Twitter has been pushing direct messaging into a full-fledge messaging platform. It recently removed the 140-character limit from direct messages
Also, Twitter should be open in a tab for receiving the notification.