Favicon (short for favorite icon) is the icon showing on browser's address bar or next to the site name in a bookmark list. It will be displayed on address bar when your affiliates sign up or log in their account.
Favicon helps to make your affiliate program more professional. To know how to Add a favicon to your Shopify store, follow this guide from Shopify.
To get your Favicon URL, go to your webpage and click on the right mouse, then click on View page source
Then find type Ctrl + F and type shortcut icon, you will see your favicon URL next to it.
Copy the URL and paste to Favicon URL box: