"Her" implies location without movement. For instance, "Jeg er her" (I am here). "Hit" is like the old English word "hither" and implies motion or action. For instance "Kom hit" (Come hither). The same rule applies to "der" and "dit." "Du er der" (You are there) implies no motion, whereas "Jeg går dit" (I am going thither) implies motion.
It's literally "be so kind".
So "Vær så snill og kom hit" could be translated literally as "Be so kind and come here."
And the version with 'å' ("Vær så snill å komme hit") that has been asked about by Bronzdragon could be translated literally (but not quite correctly) as "Be so kind to come here" or correctly (but not quite literally) as "Be so kind as to come here."