The Spectres, also known as the Spectres of Indifference, are a group of lingering dark spirits and major antagonists in the trilogy His Dark Materials, setting the scenario for a zombie Apocalypse-like landscape that reigns in the world of Cittagaze, the city of the magpies.
The Spectres came to Cittagaze through a dimensional portal, when one of the First Academics was taking apart atoms, he took apart atom upon atom, and cut into the smallest atom he could find. This served as a gate to another universe, akin to Hell, upon which all the Spectres were packed inside, and burst forth upon the first incision. The Spectres flocked out, and presumably ate all the daemons of the Academics who released them. The Spectres were formidable foes, and they destroyed the civilization in the Cittagaze world, not just in that city, but on the whole world it was on.
There are multiple worlds in the Multiverse that exists in His Dark Materials. The universes are not dimensions in the sense we know of dimensions on Earth, they do not exist as time or space, for instance. The multiple dimensions in the series are more akin to a line of books on a shelf - they exist right alongside each other, and yet are very different. Each universe came to be because of one major difference - for instance Lyra's world was probably the result of the Spanish Armada conquering Britain, and the world of the mulefa rose from there being no humans at all present several thousand years ago.
The Spectres have no known world; they exist in the space between the worlds - they are parasites of the Multiverse.
The Spectres exist by flocking around one's daemon. Adults can see them, but children cannot. This is because adults gather Dust, which is sentience, and experience, and this is what the Spectres hate, so they converge on adults and eat their daemons. This causes society to stop functioning, because "at any moment a father might be taken, or a banker, and his enterprise fall apart..." and "how can lovers keep their vows?" The Spectres are intangible, and cannot be harmed by weaponry. They cannot be killed or damaged at all, save for one or two things - the Subtle Knife, asahettar, itself, because it is made to harm everything, flesh or spirit, and also human ghosts, because, being dead, they need fear nothing.
The Spectres are immortal, and it can be said Death is their downfall. Ironically the thing they want to destroy most, experience, becomes their downfall because the ghosts of the human adults can fight them and vaporize them. The Spectres don't do that and they are powerless against ghosts.
Role in His Dark Materials
The Spectres are dominant in The Subtle Knife because they have come through the gateway between worlds and eaten almost every adult daemon in the world, leaving their humans as decaying husks which have no conscience. The Spectres are invisible to children, such as Will, and this becomes apparent in a seemingly desolate, barren world. The Spectres are first mentioned by Angelica, a child refugee from the city, who says that the Spectres ate everyone and left the world barren. Her younger brother Paolo remarks they have an older brother in the city, and he says "He's gonna get -" but Angelica smacks him and this is obviously meant to be a secret.
Later, it is Sir Charles Latrom, who is in fact Lord Boreal from Lyra's world, who mentions the Spectres. He says he would go through and get the Knife himself, but cannot because the Specters would eat him, implying he has a daemon, which he does. Sir Charles asks Will to get the Knife, and Will gets the weapon after fighting Angelica's brother, Tullio, who is insane, but Will wins. Angelica's brother then goes into a coma and is eaten by Spectres and the children vow revenge.
The old man, Giacomo Paradisi, who was being held captive because he had the Knife in his possession, is released by Will and Paradisi says that Will is now the bearer. So, Will has to accept his destiny and let the old man drug himself into death because it is the only way for the old man to escape the Spectres.
The old man had told Will the Spectres fear the Knife, and this comes in useful in the quest with the witches many times. Will protects the witches from the Spectres, and the Spectres are soon revealed to be under Marisa Coulter's control. The Spectres are commanded by Coulter to fly "she makes them forget they are earthbound" and attack the witches and Lyra, and Coulter takes Lyra when she sees Will is absent. The Spectres eat the witches' daemons, and kill the witches. But Will is rescued by the angels Balthamos and Baruch.
The Spectres return in the third book, The Amber Spyglass, where they engage in the war against Lord Asriel. They have the upper hand at first, eating all the daemons on the battlefield they find, but soon the ghosts break out of the Underworld, led by Will and Lyra, and they soon begin to get torn apart by the ghosts. Soon the Spectres are all diminished in number, enough to become scarce.
It is revealed, the only way to defeat a Spectre for good is to close all the windows the bearers of the Knife have made, because each time one opens a window, they disturb Dust, creating a Spectre.
The Spectres are cruel, cold, conniving, indifferent, (hence their name) immoral, ruthless, sadistic, arrogant, and conspiring monsters with an absolute nihilistic view on life. They are supreme predators, and desire their prey above all else. They enjoy watching their victims suffer, both before and after their attacks. When attacking, the Spectres swarm round their victims akin to a swarm of piranha or bats. They exort an odd behaviour in their victim: Upon attack, the victim will try to make themselves feel important by feeling or touching stones, rocks, money, anything in the vicinity. They also hunch their shoulders back in an attempt to ignore the Spectres. But the Spectres enjoy this, because its the daemons they are after (in the case of the humans who don't have physical daemons, they suck out the daemon from within the soul). The Spectres are also very intelligent, clever enough to form armies and go to war: They can cross dimensional voids to get to their destination, literally warping space. This makes them formidable. In the final battle against the Church and the Authority, it is revealed the only weakness of the Spectres is ghosts, because mortal weapons cannot harm the Undead Spectres, but the Undead themselves can. The ghosts rip the Spectres apart in the final battle and dismember them, forcing any survivors to most likely retreat back into the interdimensional void, where they would presumably starve to death.
The Spectres are invisible most of the time, but when they reveal themselves to teenagers and adults, they become a wraith-like, misty, vaguely humanoid form which swirls around looking for prey. They swirl round victims in a smoke form and attack. The Spectres' attack is seen in our Universe as somewhat akin to OCD, or any other form of mental illness. One of the first seen victims of the Spectres was Eileen Parry, Will's mother.
The effects of a Spectre attack in our Universe seem different, as rather than killing humans outright, they play with them forever, thus making them paranoid and afraid of life, making the Spectres even more cruel.