The favicon image is the image that shows in the browser tab when the page is open. The default that comes with the script is the blue star. To change your websites favicon you will need to generate a .ico image.
A simple free site to do this is https://www.favicon-generator.org, you will need an image to begin with. A square image is best, the generator will shrink it to the necessary size. After uploading your image choose what to convert your image to, an image for all browsers or simply the favicon.ico image (what I generally use). Next uncheck the Maintain Image Dimensions box as well as the public gallery box and click the “Create Favicon” button next to your image. Download the .ico file from the generator.
Now open up your hosting and file manager, you want to upload your .ico generated image to your root folder (public_html for most). Yes, overwrite the file there already. Now go to your website, if you do not immediately see the new image in your browser it may just be your cache… use the keyboard command Ctrl+F5 to do a hard refresh, it may take a few times to see the new image in the tab.
Now in your template create a folder named backups or something similar, copy the index.php file from your template to the new folder to keep the public out, copy the favicon.ico file you uploaded to the root to this folder so you do not lose the image in future updates.