Seithr oil was a liquid substance taken from the petals of the Seithr plant, which grew on a small island in the frigid northern seas. The oil was normally harmless and mainly used for preserving pearls, but when a certain incantation was spoken over it, along with the offering of a blood sacrifice, it became a deadly, caustic poison. It ate away anything living or previously alive, if the poisonous effect was to be stopped the wound is stated in "Eragon (book)" to never regenerate or heal even with the help of the Deities. Strangely seithr oil left everything else with which it came in contact untouched. Because of this, it was frequently used by assassins and Ra'zac.
The Ra'zac used Seithr oil to torture, then murder Garrow and there also was Seithr oil on the dagger the Ra'zac use to try to kill Eragon with. Brom died from taking the Seithr oil-covered dagger for Eragon. Eragon and Brom also used shipping records of the oil to track down the Ra'zac.
Also, Eragon and Brom were able to track the Ra'zac further as Eragon found Seithr oil during their travel.
The word "Seithr" in the Ancient Language means "witch", so Seithr oil is actually named Witch Oil.
Real-world connections
Seithr oil's behavior is similar to protease, a type of enzyme that catalyzes the breakdown of protien. Since all living things contain protien, a solution of mixed proteases will destroy any living or formerly living thing that contains the right types of protien. Since protease is not corrosive, it does not affect inorganic materials.
Some real-life plants contain some protease, such as mango and pineapple, and this is said to help with digestion. Viper venom contains highly-concentrated protease, which is what kills their victims.