To my knowledge the marksman headshot bonus can only be achieved in the sniper class. Its basically extra points for killing people that are quite far away with a headshot.
To get the bonus your target has to be over 100 meters away and then every meter over 100 will get you another point. So if you killed someone 101 meters away you would get a +1 Marksman headshot, killing someone 200 meters away will give you a +100 marksman headshot bonus etc.
As far as I am aware the highest bonus you can get from this is +500 (although I cant confirm this because thats only from personal experience and never getting higher than that).
A little tip for achieving these is to hold down the fire button once you have fired the sniper rifle - this will keep the scope open so you can follow the path of the bullet and how much it dips. This will make adjusting for the second shot much easier.