White noise is a term that describes a certain noise, amidst a lack of sound, being projected over an area. The phenomenon often manifests itself as ringing in the ears, amongst other symptoms.
The vault experiment of Vault 92 involved secretly exposing the musicians in the Vault to the noise as research for possible future applications. Unbeknownst to Professor Malleus, the scientist in charge of the project, Vault 92's Overseer, Richard Rubin, exposed all vault residents to the sound in their sleep and "programmed" them with additional directives. These orders, and the commands that were fed to the inhabitants of the Vault in their sleep, came directly from Vault-Tec and were supposed to turn the vault inhabitants into soldiers who would carry out any order and feel no pain.
This experiment, like so many others initiated by Vault-Tec, ultimately failed. The white noise eventually caused the subjects to go insane, experiencing significant mental impairment, and heightened aggression that lead to the death of everybody else in the Vault.
There are several audio logs in Vault 92 concerning the mind control project. They give a backstory on how things went wrong and how the scientist slowly discovered the Overseer's true intentions.
The white noise can be initiated by hacking a computer terminal in the living quarters and selecting "Noise Flush". This will instantly kill any mirelurks that are wandering in the area.