The Serpent Stone grants the Dragonborn the ability to use a ranged Paralysis poison on opponents once every in-game day. The poison paralyzes the target for 5 seconds and does 25 points of damage. As with many paralysis enchantments and spells, this ability is especially useful when NPCs become hostile towards the Dragonborn after dialogue.
The stone can be found on Serpentstone Isle, north of Windhelm and east of Winterhold. Galmar Stone-Fist sends the Dragonborn here to initiate them into the Stormcloaks. Upon arriving, the Dragonborn must slay an ice wraith.
Galmar Stone-Fist will tell the Dragonborn that men have been sent to this location for generations to test their strength. He also says that ice wraiths are oddly attracted to this location.