In paintball terms, yes the Bud Orr Sniper and Sniper I (my first marker!) were named so because at the time they were more accurate than most other markers, as far as Bud Orr was concerned.
In reality, the word "Sniper" finds its basis in the days of old, when men went out to hunt the Snipe, which is a scrawny water bird with a long beak, but they were bloody hard to get and would often see you, long before you could get a shot in. So to be a Sniper, meant that you had very good field craft skills in order to get a shot on a Snipe.
More recently, the term is used to describe a soldier (or usually a pair of soldiers) who are deployed inside enemy lines and use amazing skills at concealment and moving unseen, coupled with deadly long range accuracy with a rifle.
Contrary to popular belief, they not only take out targets, but can also be used to simply watch an area, for days or weeks at a time, remaining unseen to gather information, which can be relayed to their commanding officer. They are also used to call in "indirect fire", providing accurate coordinates and fall of shot, from tanks, artillery and so on.
The best Snipers, were usually hunters before they joined the military and had honed their skills against wolves, bears, deer and other animals that have a much better sense of impending doom than any human.
The "Ghillie Suit", that people mentioned, was developed by hunters.
There are many available to buy ready made, but none of these are as good as a hand made one. Baring one that has IR blocking properties (harder to see with night scopes), but even those don't actually look that great for regular concealment.
Usually, a Sniper will get a "net suit", which is like a morning suit (long tails) jacnet and trousers, made of a net material, so it can be screwed up small. Then the Sniper will cut up strips of Hessian (sack material), glue them all over the back and sides (not usually the front), then rough them up with a wire brush so that they fluss up and blend together. Some of teh hessian may be dyed before they use. They will also sew on strips of green elastic, in various places, so that they can then attach local vegetation to the suit, to improve concealment.
A dude hiding in a Ghillie Suit:
http://cheapassairsoftguns.com/wp-content/uploads/2008/07/ghillie_suits-airsoft.jpg
A dude standing in a Ghillie Suit:
http://cheapassairsoftguns.com/wp-content/uploads/2008/07/big_man_size_ghillie-suits.jpg
Something that annoys me, is when you hear the term "Police Sniper" in the media etc. The Police, do not have Snipers. They have "Marksmen" and usually that describes them loosley. They are not Snipers, because they do not need to hide, seldom get shot back at, have enormous backup don't have to take shots much over 200 yards or so (certainly not 800 yards plus). A "Marksman", is a good starting point for a Sniper, but as there is so much more involved than simply being a good shot, it does not mean that a good Marksman, will be a good Sniper.
Ther, so probably a little more detailed than was required, but the question seemed to suggest that the OP did not know what a Sniper was, in any form. So now he does. Those who know me, will also know that I know (!) a fair bit about this sort of thing and will likely assume (correctly) that the above is not simply good use of Google, other than the images.
Every day is a school day