What white noise is
White noise has the same power at every frequency, so a graph of it is flat. Each octave spans twice as many frequencies as the one below it, so a flat spectrum puts most of its energy in the high octaves. That is why white noise sounds bright, like a hiss or a radio between stations. That evenness is what makes it good at covering sudden sounds.
The three differ in how power falls as pitch rises.
The three differ in how power falls as pitch rises. White is flat. Pink noise loses 3 dB per octave, so each octave carries the same energy and the sound is softer, like steady rain. Brown noise loses 6 dB per octave, so low frequencies dominate and it sounds like a deep rumble. The buttons on the player switch between them, and ocean waves, which is brown noise swelling about every ten seconds.
Masking, not magic
A steady background makes sudden sounds stand out less against it, which is why people use white noise against traffic, thin walls or a partner who snores. Studies of whether it improves sleep itself give mixed, mostly small results, so treat it as a tool for hiding noise. If you wake up to a hiss that is too sharp, pink or brown noise is a gentler place to start.