Banshee Circuits were components of TARDISes, emergency defence mechanisms used as a last resort when all other systems had failed. They allowed a TARDIS to use whatever resources were available to ensure the survival of the ship and its crew. They also functioned as the ship's flight recorder. When the Doctor's TARDIS was attacked by the Process and collided with the Time Scaphe, it activated its Banshee Circuits and reconfigured itself into a SARDIT, while the Circuits themselves took on the form of the Banshee, appearing as the Seventh Doctor in blowing robes and a collar. After the Process was destroyed, the TARDIS returned to its earlier form. (PROSE: Cat's Cradle: Time's Crucible)
The appearance of the Banshee is similar to the Cloister Wraiths. (TV: Hell Bent)