What brown noise is
It's also called Brownian or red noise. Loudness falls with frequency faster than in pink noise: 6 dB per octave. What's left is mostly low frequencies, so there's almost no hiss.
The name isn't about the colour but about Brownian motion, the maths behind this type of random signal.
Why people choose it
Brown noise is good at covering low sounds: traffic rumble, the neighbours' bass, voices through the wall. People often play it for work and study, because it doesn't tire you even after hours.
Social media recommends it for focus, including for people with ADHD. There's little serious research on brown noise specifically, so see how it works for you.
How to listen
At low volume. For sleep, set the timer; for work you can keep it on in the background with breaks. For something brighter, try pink or white.