Gorgon Blood is a spoil of war, left behind from killing a Gorgon. According to Stheno, blood from the right side of a Gorgon's body can heal any injury, while blood from the left side of a Gorgon's body will cause a painful death.
When Stheno and Euryale chase Percy Jackson, Stheno reveals to him that blood from their right side can heal anything, but blood from their left side is lethal. Percy manages to escape from them long enough to get to the Tiber River. He then uses the water to rip the Gorgons apart as they are unable to reform unless connected to the earth. As their essence is washed away, Frank Zhang reaches into the river and pulls out two bottles and put them in his pocket. When Percy notices the movement, Frank gestures to him that they would speak of it later.
Later in the book, Percy decides to make a deal with Phineas. Each of them must drink from either one of the two bottles of Gorgon blood. Percy claims he is unable to tell either one apart. He relies on Gaea to trick Phineas into drinking the wrong bottle. Phineas disintegrates, whereas Percy only feels a burning in his throat and a stomach ache that quickly passes. The bottle of Gorgon blood did not return Percy's memory immediately; instead, Percy slowly regained it throughout the rest of the quest.