In Halo 2 through Halo: Reach it is represented by purple crosshairs on a six-pointed gold star. In Halo 4 it is represented by white crosshairs on a blue circle on top of a grey four-pointed star.
After you kill an opponent with a sniper weapon, a message appears on your screen that says: "You sniped (player)".
Earning 10 Sniper Kill Medals or Headshot Medals in a Halo 3 campaign level or free for all ranked playlist match unlocks the Headshot Honcho achievement.