For historical reason web sites favicon are typically ICO files.
An ICO file can contain multiple bitmap images of different dimensions.
GIMP can generate such an ICO file from multiple layers.
Whether you have your various size icons as PNGs or JPEGs or a single SVG file, you can import them...
Those icons your web browser usually show on its tabs are called favicon in web developer jargon. They notably allow users to easily navigate their browser’s tabs while exposing them to your brand.
Funny enough XenForo v1.5.12 did not seem to provide any built-in support for favicon.