Fallout, Fallout 2Edit

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.

Fallout 4Edit

Range is now a weapon stat that determines the furthest distance that a particular weapon will be able 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 (notably Ranks 2 and 3) can compete with rifles, usually at the cost of lower Accuracy. When applying Range mods to your weapons, you can test it by going into V.A.T.S. on your settlers or turrets, turrets being the better choice due to being stationary; your queued shots will indicate less damage once you are past the Range limit.

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.