A bleed effect is essentially a DoT applied to a character or monster that does not require continous casting.
The bleed effect obviously indicates that a target is losing health over time due to blood loss. Certain skills can sometimes synergise with this effect, like increasing damage while bleeding, or increasing the caster's ownhealth while target is bleeding.
If the caster receives health from damaging, then that is normally referred to as a leech effect.