Brown noise is one of the many colors of noise, which also include white noise, pink noise and blue noise. However, brown noise doesn't get its moniker from the color — it's actually named after botanist Robert Brown, who discovered Brownian motion (random particle motion) in the 1800s.
Brown noise is also known as Brownian noise because its change in sound signal from one moment to the next is random.
Unlike white noise, whose spectral density (power per Hertz) is even throughout all frequencies, brown noise has a spectral density that's inversely proportional to its frequency squared — in other words, its power significantly decreases as its frequency increases.
As a result, brown noise has a lot more energy at lower frequencies than it does at higher frequencies. Brown noise is sometimes referred to as red noise because it's somewhat analogous to red light, which has a low frequency.
To the human ear, brown noise is similar to white noise, but is much deeper — it has the sound of a low roar not unlike that of a strong waterfall.
Though the names are similar, brown noise has nothing to do with the mythical brown note, a hypothetical low-frequency sound said to cause people to lose control of their bowels.