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. In return, chance to Bleed is a Primary affix, while other chance on hit affixes are Secondary.
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.