Banshees are attuned to a level of the universe nothing else is. This network broadcasts supernatural messages concerning death to a banshee. They are able to connect to this network and issue messages of their own, broadcast their own 'whispers' surrounding death, or communicate with other banshees.
This network can be accessed through 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.