Why one image is never enough
A browser tab is about 16 pixels square, a bookmark bar 32, a desktop shortcut 48, an iPhone home screen 180, and an installed web app wants 192, 512 and 1024 for splash screens and stores. Handing a browser a single 1024 px image and letting it scale down gives a blurry or aliased result, because browsers scale icons with whatever filter they have at the moment - so the conventional answer is to ship each size already sharpened down properly.
favicon.ico is a container, not an image: one file can hold the 16, 32 and 48 px icons and the browser picks the one it needs. This page writes exactly that, with each size stored as a PNG inside the container - which is what Windows Vista and everything newer reads, and what keeps a 48 px icon crisp on a high-density display.
Favicons are also square. A wide logo is cropped to its largest centered square first, and the crop anchor decides which part survives - center for most marks, left or right for a wordmark whose first letter carries the identity.