A envelope icon will be displayed in Windows Taskbar when a new email message is received in Outlook 2010 and Outlook 2013. This is the default behaviour of Outlook and in case if this is not displayed then you can enable this feature using mail Options available as part of Outlook Settings.
Listed below are the steps to show or hide nee message icon in the taskbar in Outlook 2013 and Outlook 2010
Step 1: Click File menu and click Options in the menu list.
Step 2: In the Outlook Options window, navigate to Mail tab.
Step 3: Under Mail settings, scroll down to Message arrival section and mark/ unmark the checkbox with caption as “Show an envelope icon on the taskbar”
Step 4: Click OK button to confirm and save the changes.