What you are hearing
Brown noise loses 6 decibels per octave as the frequency rises. Almost all its energy is below 500 hertz, so it sounds like a river heard through a wall or the cabin of a plane. It is named after Brownian motion, not the colour.
What it does
There are no controlled trials of brown noise specifically. What is well established is masking: other people's speech is the single most disruptive sound for tasks that use working memory, and steady broadband sound covers it. The "irrelevant speech effect" has been replicated since the 1970s, and it does not matter whether you can make out the words.
Set the volume just above the sound you are covering and no higher. If you can feel it, it is too loud. If you stop noticing it after a minute, it is right.
When to pick something else
On laptop speakers brown noise turns to mud; choose rain. If a low rumble makes you drowsy, choose pink noise or a natural recording. If you have never tried noise for focus, start here for a week, then compare.
Salamé & Baddeley (1982), Journal of Verbal Learning and Verbal Behavior, 21(2). Full comparison: our article on brown, white and pink noise.