Alternate air is provided on fuel injected piston engines as just that - an alternate air source.
When the normal, filtered, air intake isn't doing it's job, you can switch to alternate air, which provides an unfiltered source of air (usually from inside the cowl).
If impact ice has iced up your air filter and you can't get manifold pressure - go to alternate.
If a swarm of locusts have blocked your filter - going to alternate will give your engine air (and probably few locusts.) etc.
You would never use it in dusty conditions - that is what an air filter is for! Barring an emergency, of course.