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.