Physical damage is the most common type of damage, associated with white, red or black colors. All the hero classes and almost all monster types have a physical damage attack as their default attack. Any melee blow or kinetic missile will count as Physical. If damage type of a weapon or skill is not specified, it is most likely Physical. Bleed effects use Physical damage type as well. In addition, Demon Hunters, who use the power of shadow itself, also deal Physical damage when they unleash hatred of the pure darkness. Necromancers, in turn, use the powers of Blood and Bone to deal Physical damage.
Some skills, hero and monster alike, deal physical damage and may also do another type of elemental damage. While other types of skills/attacks of elemental damage are commonly reduced or nullified by Elemental resistance or immunity, Physical resistance was introduced in Diablo II, but it was rarely shown, and it was not noted on the character sheet. However, it is a full-fledged resistance in Diablo III.
In Diablo II, its chance to hit is reduced by defense (unlike other spells), and several monster types, especially in later difficulties, have Physical immunity or resistance. Items with the property 'Damage reduced by X' also can protect against it.
In Diablo III, it is used by Barbarians, Crusaders, Necromancers, Demon Hunters and Monks, as well as by Witch Doctors (their pets' melee attack mostly, unless other damage type is chosen), but never by Wizards.
Critical Hits from Physical damage may rip the target's flesh from bone, tear is apart, slice and dice, decapitate, sever in half etc.
Andariel's Visage, Stone of Jordan, Lidless Wall, Doombringer, Heart Slaughter, Swamp Land Waders and Holy Point Shot are the items with unconventional bonus to Physical skills damage. There is no amulet that would make a character immune to Physical harm.