Favicon is a small image (an icon) that represents your website. A favicon is most often located in a browser tab, the address bar, bookmarks, browsing history, etc.
A favicon might not seem that important but it’s a great way to personalize your website and have something that represents you/your business on the web. Think about this, there are many places on the web that you’ll see the alphabet “G” but you can easily tell when a particular “G” represents Google. The same goes for other companies like Yahoo, Microsoft, Apple, etc.