Agramon is the Greater Demon of Fear who appeared in the City of Ashes. This demon doesn't have a physical form; it is described as a mass of gas at first. The power of Agramon is he appears to you as your greatest fear, and your terror of him will quickly kill you.
He was summoned by a young warlock called Elias who was hired by Valentine Morgenstern to summon Agramon. When summoned, Agramon breaks free from the pentagram which was supposed to keep Elias and Valentine safe because demons are trapped within it and can not escape. However Valentine, aware of what Agramon was capable of, did not warn Elias that because Elias's biggest fear was of a demon breaking free from the pentagon, Agramon could free himself. Agramon frees himself and kills Elias, but not Valentine as Valentine can control him as he possesses The Mortal Cup.
Agramon first appears to Jace as total darkness in the Silent City, since Jace had suddenly began feeling very scared as an effect of the night at the cell in the Silent City. He is the reason why Brother Jeremiah runs screaming in terror down to his cells.
It next appears to Jace as a very injured Clary, his biggest fear, when he sneaks onto Valentine's ship.
In the battle at Valentine's ship, it appears as Valentine to Jace and taunts him about Jace's similarity to Valentine. Jace, wearing the Fearless rune that Clary created, later kills Agramon, but not without difficulty as he is not sure if it really is the demon, or if it's his 'father'.