A vanity address is a personalized URL for your Apartment Therapy Marketplace corner. So instead of the URL showing your member ID, you can update it to show your name or the name of your business.
If you would like to set a Vanity URL for your corner, you can do so by logging into your account and accessing your About Me settings here.
A green check mark next to your entry will mean that the vanity URL you have entered is available and will be saved for you once you click on Update. A red X means that the vanity URL you have entered is already taken by someone else and therefore cannot be used.