The reference of the file favicon.ico is given in _layout.cshtml or in any of your master page.
Debug your application,See the image for reference:
you can see the blue and white colour small icon on the left side of a tab. This is default asp.net website favicon which is used by visual studio.
If you want to add a favicon in your website then you have to create a small icon first. Suppose you are having .jpg or .png image that you want to add as favicon, then first you need to convert that image in .ico format, otherwise, favicon will not work in some browsers.
Internet Explorer will not show the favicon if the image is in the .jpg or .png format.
Two links are provided so that application can run with most of the browsers. For example,Firefox and chrome will work with either of the links but Internet explorer will work with rel=”shortcut icon”,so if you will use both the links then application will work in almost any browser.