You can choose to turn email notification on or off. Turning them on allows you to see a message pop up from your system tray.
When you click on the notification it opens that email in Mailbird when it is minimized or not the active window.
To adjust your email notification settings:
1) Go to the Mailbird menu in the top left of the main window.
2) Select "Settings"
3) Click the "General" tab
4) Check or un-check the "Notifications: Show tray notification when receiving a message" box.
You will see the new email message notification in your system tray that you can click on when Mailbird is minimized to open that new message.