In reply to Jeffrey.

Site icon is a combination of the favicon and the icons used for bookmarks in mobile devices. It's the icon that represents your site in a number of different ways.

It is used as the favicon, yes, and it needs to be large because small icons look awful on high resolution screens.

Basically, 512 is the common recommended size for all of them. Even for favicons, on HiDPI devices (like retina screens), the icon displayed can be much sharper and cleaner if it's a higher resolution.