Vision (Basic)
As with all units in StarCraft, your sniper has a vision radius around it that allows you to see enemy units nearby.
Vision is shared with teammates, which is why teamwork is so essential!
Trail Vision
Vision is only lost periodically, so you can move around and have a "trail" of vision left behind you for some time. This is the main way of seeing enemies without them seeing you! If an enemy wanders in your trail vision you can easily NL them. If they're not ready for it they will probably die.
Trail vision can let you shoot around obstacles like walls and pillars. See the Blinding section for a more thorough explanation.
Death Vision
There is also a very small area of vision left around your body when you die, which can last longer than the trail vision. This is your death vision.
Killer Vision
If you are killed from somewhere you have no vision of, you'll get a glimpse of your killer with some "killer vision". However, your teammates cannot see this killer vision, so don't expect them to shoot an enemy standing there unless they move out into your trail/death vision.