The Prophecy of the Seven is the Prophecy on which the whole Heroes of Olympus series is based. This Prophecy was revealed at the end of the Book: Percy Jackson and the Olympians: The Last Olympian. It goes as such:
Seven half-bloods shall answer the call.
To storm or fire, the world must fall.
An oath to keep with a final breath,
And foes bear arms to the Doors of Death.
Line by line analysis:
It says that there would be seven demigods who will be going on the quest. Hence the name of the Prophecy is "The Prophecy of the Seven".
The world, which later in the series, infers to the Primordial, Gaia, or Gaea, would end by the hands of "Storm" or "Fire". This narrows down 3 out of the seven demigods. Who are Percy Jackson, Jason Grace and Leo Valdez. This line also means that the person to kill Gaia will die in the process. In the end of the series, this turns out to be Leo Valdez, who later is resurrected by a potion made by the God of Medicine. The potion is called as the Physician's Cure and was created by Asclepius.
Leo had Swore on the River Styx to rescue Calypso from the island of Mythical Place: Ogygia. After the main battle ends, Leo goes on a quest to save Calypso and is able to do that with the help of his Magical and Mechanical dragon, Festus.
Gaia had opened the Doors of Death and in the House of Hades, Percy and Annabeth venture through Tartarus to and team up with a Giant named Daemson and "Bob" the Titan to close the doors. Hence proving the last line as well.