can anyone explain what falloff damage is and what the benifits of falloff mods are

[Cavadus]

Falloff DMG is the damage that you deal when your weapon is outside the optimal range. So, if you have a mod that deals +8 falloff dmg, then your weapon deals [x] dmg when out of optimal range and with the mod it's [x] +8. Hope that helps.

No, this is incorrect.

All weapons have a range threshold of X meters. The further a projectile travels past said threshold the less and less damage it inflicts on a target.

The +falloff mods do not add additional damage, they extend the range of threshold at which maximum damage is still applied to a target.

I like to engage at the longest distances possible so I run my weapons almost exclusively with +falloff barrels unless it's something like a Wolfhound pistol where I just pile onto the already insane crit multiplier.