In essence, noise is a randomly changing, chaotic signal, containing an endless number of sine waves of all possible frequencies with different amplitudes. However randomness will always have specific statistical properties. These will give the noise its specific character or timbre.
If the sine waves’ amplitude is uniform, which means every frequency has the same volume, the noise sounds very bright. This type of noise is called white noise.
If the amplitude of the sine waves decreases with a curve of about -6 dB per octave when their frequencies rise, the noise sounds much warmer. This is called pink noise.
If it decreases with a curve of about -12 dB per octave we call it brown noise.
So we have all these funky names for noise, even though you need to understand their characteristics, but what are they used for?
White noise is used in the synthesizing of hi-hats, crashes, cymbals etc, and is even used to test certain generators.
Pink noise is great for synthesizing ocean waves and the warmer type of ethereal pads.
Brown noise is cool for synthesizing thunderous sounds and deep and bursting claps. Of course, they can all be used in varying ways for attaining different textures and results, but the idea is simply for you to get an idea of what they ‘sound’ like.
At the end of the day, it all boils down to maths and physics.