The Sniper Rifles skill represents a soldier's skill to aim a weapon very accurately, provided the weapon is designed for that. Most weapons used with that skill are indeed sniper rifles, but there are exceptions --- long range, high accuracy fire mode of any weapon is bound to require Sniper Rifles skill.
Character needs to hit enemies 3 times to gain one point of this skill.
Being able to "reach out and touch someone" can be incredibly useful, at least for the outdoors portion of a mission. Many squads have a dedicated sniper. This individual will generally go toward the the point of the map offering the best visibility, usually a rooftop or hill. Note that the Headshot fire mode causes more damage than any other weapon than the Particle Beam Cannon, and will be more necessary as the enemy gets better armored.