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."