Fallout, Fallout 2
Range is the farthest distance (in hexes) that a weapon can shoot. No matter how skilled with that weapon, one can never fire it beyond that distance without the help of an appropriate perk or other special ability.
Range is a weapon statistic that determines the furthest distance that a particular weapon will deal its maximum damage outside of V.A.T.S. and additionally affect the chance to hit a target when using V.A.T.S. Rifles tend to have the longest range modifiers, with the exception of shotgun-type weapons that fall off fairly quick. Pistols used with the Gunslinger perk (Ranks 2 and 3) can compete with rifles, usually at the cost of lower accuracy. When applying range mods to weapons, one can test it by going into V.A.T.S. and selecting settlers or turrets, turrets being the better choice due to being stationary; queued shots will indicate less damage once one is past the range limit.
When it comes to hitting targets, range is virtually meaningless in real time shooting; any missile launcher with a low range stat will still reach targets that ballistic or energy weapons with a far higher range cannot. However, range will drastically affect weapon damage, particularly if firing a weapon past its modded range value.