Order alerts appear as a numbered red oval next to the Profile icon in the top right of your ShipStation screen. These alerts can indicate several things, including:
Click the profile button and choose View Alerts to view details about the order alerts.
This pop-up menu will show a list of the alerts.
From here you can click on the order to view or dismiss the alert(s) altogether.
Dismissing an alert will permanently dismiss it for ALL users on your account, not just the user you are logged in as.