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Usually it points to the fact that you leech some hitpoints from the enemy with each hit.
It depends on the value of the regeneration.
For instance, if it is +1 (or how it is descriped) it means for everytime you hit, you heal 1 point of damage.
Vampiric Regen is damage regenerated when you land an attack. This is limited to a per-round basis.. so you only get (say) 3 hp a round with a +3 vampiric regen weapon, even if you hit them five times.
Vampiric regeneration is bonus magical damage that act negative to enemies<leech HP> and heal your wounds( if you are uninjuried it will not work)
Ascorian double axe or Aribeth's bastard sword is an example of such a weapon.