What you are hearing
White noise carries the same energy at every frequency. Because hearing is most sensitive in the middle of the range, it feels bright and, at volume, sharp. It is the reference against which pink and brown are defined.
The study people mean
Söderlund, Sikström and Smart (2007) played white noise to children with and without ADHD during a memory task. Children with ADHD did better with noise; children without did worse. The proposed mechanism, stochastic resonance, is that a nervous system running at low arousal benefits from added input. Later work has been mixed, and nearly all of it is with children. It is interesting, not a prescription.
Practical use
White noise is the strongest masker for high-pitched intrusions: a kettle, a printer, keyboard clatter. For speech, brown noise does the same job at a kinder level. Keep white noise low; it is the colour most likely to tire you.
Söderlund, Sikström & Smart (2007), Journal of Child Psychology and Psychiatry, 48(8).