What is the small site-specific image that appears in the browser tab for some websites? How do I add one to my website?

What is the small site-specific image that appears in the browser tab for some websites? How do I add one to my website?

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It is called the http://favicon.io file. Just search for a favicon creator on the web, choose the image you want to turn into the icon then upload it to the root directory of your server.