A banshee experiences premonitions of one's impending death. Their predictions appear to them as factors that will be the causal factor of near- or affirmative death experienes. A banshee's predictions are not set in stone and do not always come true.
Lydia Martin was born a banshee, though she was initially unaware of her trait. In Season 2, after she was bitten by alpha werewolf Peter Hale, Lydia's powers came out and began to manifest. In Season 3, Lydia was finally identified as a banshee by Jennifer Blake. Lydia, now aware of and having accepted her abilities, uses them in her role in Scott's Pack to solve mysteries, determine when, where and how death occurs, to learn how to prevent an oncoming murder or catastrophe from happening.
Another banshee, Meredith Walker appears in Season 3 and is a patient at Eichen House. Meredith acts both as an ally to Lydia and the pack, teaching Lydia how to hone her powers as well as an anti-villain, being the benefactor in Season 4.
Lorraine Martin, Lydia's paternal grandmother, was also a banshee, whom was instrumental in producing the deadpool. In Season 6, a middle-aged, extremely powerful banshee named Lenore appears who was the sole survivor when the Wild Hunt appeared in her town and erased every resident.
Banshees are human in appearance with no power to shapeshift nor any superhuman abilities. As such they have the same physical tamra and mortality as the regular human being.
Though banshees have supernatural abilities, they are not actually supernatural beings as in the manner of a kitsune or a werewolf, they are not controlled by the supernatural. They are instead able to access and manipulate the preternatural forces to their will. Due to this, a banshee is immune to general supernatural phenomena. Mountain ash has no effect towards them and they can even touch or cast barriers out of the wood themselves. Similarly, they are not affected by an alpha shifter's bite or a kanima's neurotoxin. In Season 6, it is shown that banshees also cannot be taken by the Wild Hunt, due to Ghost Riders having an instinctive avoidance of them.
A banshee, due to being able to access the supernatural have a multitude of psychic abilities that work in tandem with their premonitions, particularly clairvoyance, astral projection. A banshee is able of sharing a psychic or telepathic connection with fellow harbingers of death, like a hellhound.
Their Scream can only be heard by another banshee or those with a supernatural sense of hearing. In 3x09 - The Girl Who Knew Too Much, Lydia let out a Scream because she was about to be murdered by Jennifer Blake, which lead to Jennifer identifying her as a banshee. They can be heard from miles away, even to a werewolf's magnitude of hearing.
A uses uses their Scream like a lever over their abilities and hearing. The Scream is used to drown out all other surrounding sounds so a banshee can focus on what only they can hear. In 3x15 - Galvanize, when Lydia, along with Scott's Pack, were looking for serial killer William Barrow who had kidnapped Kira Yukimura. Lydia was hearing a sound similar to flies, and had an great urge to let out a Scream which she did. Right afterwards, the buzzing sound amplified. Lydia realized it wasn't the sound of flies she was hearing; it was the buzzing of electricity. She then pieces together that electrocution would be the cause of Kira Yukimura's planned murder by William Barrow's hand at a power substation.
In 3x19 - Letharia Vulpina, Lydia, in frustration, threw Talia Hale's claws while Screaming unintentionally, giving her focus into one point, sending the claws flying across Derek's loft then becoming embedded in the wall. In 5x01 - Creatures of the Night, Lydia, using her hand-to-hand training, specifically strikes, kicks and grabbling, is able to project powerful offensive Screams as high-powered sound beams multiple yards outwards from her frame. Meredith also once used her voice after ferociously slamming her fists on a desk, then channelled her voice, creating an explosion, with glass shattering, destruction happening around her all at once "like a bomb." Once a banshee is powerful enough, the Scream can become so dangerous, that without control, it could kill everyone nearby and even the banshee herself.
A banshee scream is also used to cast spells. In 4x11 - A Promise to the Dead, Lydia was able to wake Deaton up with her Scream when he was incapacitated, stuck in a vegetative state by Valack's telepathy. In 5x20 - Apotheosis, Lydia Screamed Mason's name at the the Beast whom had been revived by using Mason as a vessel. The resulting spell Lydia cast using her Scream, reversed the Dread Doctors' conversion process to revive the Beast, freeing and separating Mason from the Beast's essence envoking the myth that to "cure a werewolf, you call out their Christian name."
A banshee's power generally manifests as the ability to hear. They hear voices or noises in their heads that only they can receive and translate. These voices they hear are the messages of their own banshees. The sounds they hear are what a banshee receives to divine further information surrounding death.
This network can be accessed through inexplicable conduits that produce soundwaves; plucking piano strings, listening to inactive phones as by Meredith Walker or listening to a record player in the case of Lydia, and her grandmother Lorraine Martin.
In 3x23 - Insatiable, Lydia had intended to warn the Pack not to look for her, because she'd predicted Allison Argent's impending death. This warning was relayed to them by Meredith. Lydia had subconsciously tapped into the whispers' network and Meredith had received the message.
In 4x04 - The Benefactor, Lydia, with the record player on, tapped into the network again. From her eyesight she saw the outlines of multiple faces emerging from the walls of the study at her grandmother's lakehouse, which were issuing whispers. These faces she saw are likely to be the source of the banshee whispers.
Harbinger of Death
Main article: Death Omens
Banshees cannot only predict death, they can identify where death occured, and sense someone's death becoming aware of their passing away just by 'feeling' it.
During Season 2, Lydia would experience fugue states, after her powers were activated, though she didn't understand why they were happening. One fugue state occured in Omega and she was confirmed to be present to sites linked to death: the Hale House, where the Hale Pack was killed and Beacon Hills Cemetery. She would also be drawn to dead bodies, murder scenes, and receive visions or noises indicating how, where or when someone would die.
In 4x03 - Muted, Lydia was drawn to the Walcotts' family house, not only because of the family being murdered, but because the Walcotts were wendigos and fed on rationed dead bodies. Just like at the Glen Capri she makes out the same human faces upon the wood of the family's secret panel leading to their 'game' locker.
When Meredith and Peter Hale were simultaneously comatose, both were placed in the same room, Meredith was involuntarily synchronized with Peter's thoughts for months. Peter was in his vegetative near-death state and was subconsciously rambling. In Meredith's mind's eye it was as if Peter was standing right next to Meredith, leaning over her, whispering into her ear.
In Required Reading, Lydia realized a Banshee prediction she'd had was a someone else's memory, one she'd tapped into. That of a test subject of the Dread Doctors while they were examining him in the past, who'd die at the hands of Theo Raeken.