Weapons can have various effects on them. This can include increased accuracy, power, fire rate, magazine size, and others.
Some weapons have effects that increase base stats, such as power, accuracy, and fire rate. Certain Manufacturers specialize in certain effects, such as Jakobs guns have increased power, while Hyperion has increased accuracy.
Some weapons have more conventional effects, but do not actually affect stats. This includes increased magazine size, increased melee damage, increased projectiles, increased reload speed, increased weapon zoom, and Burst Fire. Burst fire causes 1 shot out of the magazine for every 100% to come out full-auto; similar to the three-shot burst of some Combat Rifles. This usually applies, however only to semi-automatic weapons, such as shotguns or Rocket Launchers. Increased projectiles usually applies to shotguns, giving them extra pellets, however it can be used on any type of gun. This can be done using 1 ammo used per projectile, or 1 ammo for 1 shot. (Ex. A shotgun can fire 9 pellets with 1 shell, but an SMG may use 2 SMG bullets for 2 SMG projectiles with 1 pull of the trigger.)
Some effects are crypic messages, which give a hint on what the effect is. In the case of Eridian Weapons they simply give some insight on what the gun does, as the only other info the player gets from it is the base stats. Sometimes, these can simply be a humorous way of reiterating effects already stated ("I spy with my little eye..." implies great weapon zoom, which it states); others are effects themselves. ("Holy crap! It shoots rockets!" shotguns fire rockets instead of a pellet spread) Other times they don't even mean anything; they are simply put there to be humorous. (The Clipper's ""Don't drop it; might lose a toe", for instance.)
See Special Weapon Effects for a list of these effects.