how to : function.php of a theme

hi

can you explain when function.php of a theme is called ?

in fact, in this file, I change thumb size on the fly as the device is a mobile or not (of course I can use css to resize).

by default and for desktop device, thumb size is 220
if mobile device, thumb size become 350.

but sometime, thumb size is not changed (it remains 350 on desktop device)

I whish to understand why.