This is damage from gunfire or explosions with shrapnel, or other chemically (or electrically) propelled projectiles. It includes magnetic linear accelerator projectiles (rail guns) and missiles. Explosions that do not have shrapnel are considered energy damage. Fire and ray-beams and the like are considered energy damage. Arrows and bolts from bows (even crossbows) are considered melee damage.
The primary reason for differentiating melee and firearm damage is armor.