Bleed is a form of Damage Over Time in Diablo III and Diablo IV. Generally, its damage type is Physical. Bleed is based on the Open Wounds effect from Diablo II.
Diablo III
A chance to cause bleeding can roll as a Primary affix on a weapon or a quiver. It is an 'on hit' effect, subject to Proc Coefficient, that can trigger on any damaging attack.
Bleed usually inflicts a percentage of weapon damage, mostly anywhere from 300%-400%, over 5 seconds. It cannot critically hit, but increases damage proportionally to the Critical Hit Chance / Damage ratio. It also fully benefits from Physical damage increasing traits. Legacy items could sometimes roll a fixed amount of damage over time, but as of Patch 2.0, most Bleed effects depend on weapon damage.
Unlike other 'on hit' effects, Bleed has a very high chance to occur, up to 39% at level 70, and may considerably increase total damage. The tradeoff is that a chance to Bleed is a Primary affix, while other chance on hit affixes (which tend to trigger Crowd Control effects) are Secondary.
Some skills, like Rend and Exploding Palm, are treated as Bleed effects, even if they deal damage of any type other than Physical.
Note that generally the same Bleed effects (same rune and same character) on the same target do not stack, so applying the already active Bleed effect to that the same target will only renew its duration.
The only case in game where Bleed classification is relevant is the Pain Enhancer Legendary gem, which (at rank 25+) grants increased attack speed for every bleeding enemy in close proximity. This does include enemies suffering from conventional Bleed on weapons and quivers, Exploding Palm, and Rend, in addition to the gem's own Bleed effect.
Diablo IV
Bleed returns as a mechanic of the Barbarian class. Most Warlord skills apply it upon dealing damage.
Gushing Wounds, Cut to the Bone and Blood Thirst talents are specifically designed to enhance Bleed effects. Ironically, despite most Bleeding skills being of Warlord tree, all three of these talents are located in the Berserker tree instead.