The Amulet of Samarkand is an extremely potent magical artifact. It is an amulet, a passive magical object designed to protect its bearer from certain forms of attack, in the case of this one, magic-based assaults from even the strongest magic and demons.
The Amulet of Samarkand, as an amulet, cannot be activated or used consciously by its owner, it can only be borne, and will work when certain conditions are met. These conditions are narrowed down to any form of magic-based attack; all magical assaults, energies, and when the amulet is actually being worn, spirits are drawn inside the amulet and absorbed.
The amulet will not, and is unable to protect one from physical or non-magical assault. If one were to fire a fireball at the bearer, the attack would be drawn into it without harm to the bearer, as displayed by Arthur Underwood when attempting to attack Simon Lovelace. The amulet will not protect one from "being brained by a brick", or "stubbing your toe".
Bartimaeus mentions that it must contain a demon with equal if not more power than Ramuthra as it is able to easily absorb the magical disturbances created by Ramuthra being in this realm.
The Amulet was originally made by an Asian shaman many centuries ago, and was given to a local princess as a gift. The amulet was found by a Russian archaeologist in the 1950s, and through a series of events found its way into the hands of the British Imperial Government. Up until its theft by Simon Lovelace, it was kept by a government magician named Beecham, who was killed by Verroq (known as "The Mercenary") when he stole it on Lovelace's orders.
It was then passed to Lovelace from Verroq. Nathaniel would later order Bartimaeus to steal the amulet from Lovelace, and hide it in the study of his, Nathaniel's, master, Arthur Underwood. Bartimaeus isn't sure what demon or demons are stuck inside the amulet; all he knows is that they are extremely powerful and that it makes the wearer invulnerable to magical attack. The secrets of how to make the amulet were lost to time, although Bartimaeus mentions that it must have been a hard task to imprison the being(s) inside.
Lovelace would expend much effort to retrieve the amulet, even going so far as sending two of his strongest Djinn to break into the Tower fo London to break Bartimaeus out. Lovelace's agents would track Bartimaeus to the home of Underwood, and subsequently kill Underwood and his wife after retrieving the amulet from an intimidated and bewildered Underwood.
Failing to kill Nathaniel too, Lovelace implicated him to the deaths of the Underwoods, and set out to Hedlam hall to use the amulet in his plans. Luring the top echelons of the government to the hall for a conference, Lovelace wore the amulet when he used a summoning horn to summon the great demon, Ramuthra, to kill the government magicians. Through the machinations of Nathaniel and Bartimaeus, Lovelace lost the amulet again, and was subsequently eaten by Ramuthra. After Nathaniel dismissed Ramuthra from the room, he returned the amulet to the hands of the Prime Minister, Rupert Devereaux.
The Amulet is only mentioned during the events of The Golem's Eye once when John Mandrake (Nathaniel) attempts to use the fact that he saved the Prime Minister and gave him the amulet to evade being imprisoned in the Tower of London.
In Ptolemy's Gate, the Amulet, along with other notable items such as the Staff of Gladstone, had been sealed in the Vaults of Whitehall. John Mandrake would later view the amulet. Near the end of the book during the Great Spirit Rebellion, Nathaniel would descend again into the vaults, and claim the amulet and the Staff. The amulet protected him against the terrible pestilence that guarded the room, which killed even Verroq, who had extreme magical resilience. After using it to escape the room and make his way up to an office where Kitty had used the Gate of Ptolemy to converse with Bartimaeus in The Other Place, he gave the amulet to Kitty to protect her. The amulet would save her from one of the spirit hybrids.