You have mastered the firearm as a source of pain. With this perk, any successful hit in combat with a ranged weapon will be upgraded to a critical hit if you also make a Luck roll. It adds another Luck roll of (10*Luck). 10 LK means every hit is automatically a critical hit.
With the Sniper perk, your chance to hit an opponent’s head in V.A.T.S. is increased by 25%. As with most perks that increase your chance to hit in V.A.T.S. this bonus is multiplicative, not additive. This means that if you had a 20% chance to hit an enemy's head without the perk, you would have a 25% chance with the perk.
In Fallout: New Vegas this perk is useful for counter-acting the Fast Shot trait.
In Fallout Tactics, version 1.27 does not produce the advertised result of the Sniper perk. The perk is obtainable but appears to be bugged (tests with 10 LK have failed to produce any noticeable increase in critical strike rate, which should produce a 100% critical strike rate with 10 LK and the Sniper perk). It is possible to fix this bug by hex editing BOS.exe file 4C->6C at the address 004A6C4C. [verified]