A marksman is someone who is excellent at shooting a gun. A skilled marksman hits the bull’s eye every time.
The word mark is from the Middle English word for “target,” so a marksman is a man (or woman) who has excellent aim and shoots a target. In many westerns, the hero is a marksman capable of hitting a small target that’s far away. In real life, police officers and members of the military are trained to be marksmen. Women can be marksmen, too, but if the name bugs you, call them sharpshooters.