Chrome makes it available to websites providing a PWA manifest, I believe. Firefox doesn't really have it on desktop yet, though there's a button and support for it on Android. Shortcuts on the desktop get added to where your computer would normally place these icons, be it your desktop, start menu, dock or apps folder.

You can sort-of replicate the behaviour by creating a shortcut to "chrome --app=https://www.example.com" for websites that don't offer it.