This feature displays a configured icon next to a category if a listing has been added to that category within the "new" listing time configuration made in the store. You'll find the configuration to set the time limit within which the new icon will display here within the admin tool:
SITE SETUP > BROWSING SETUP > "New Listing" Time Limit
You'll find the configuration to set the icon image to use here in the admin tool here:
SITE SETUP > BROWSING SETUP > "New Listing" Icon Url
Both of the above are shown in the following screenshot: