The Serpent birthsign gives the player the Serpent spell to cause a slow but potent poison on touch, while simultaneously curing yourself and dispelling magic from yourself. Casting this spell costs 100 points of Fatigue.
This spell can only be used once a day.
(Summary and picture from Official Elder Scrolls Site)
The Serpent spell is extremely weak, even at low levels. Alchemy will allow you to get much better poisons.