It has to do with the power of the signal at different frequencies. White noise is "pure" noise in the sense that it has an equal power at all frequencies. Other colors of noise have different power distributions: blue noise has a power that grows linearly with the frequency, pink noise has a power that's inversely proportional to frequency, etc. The color names come from what you get if you map the same power/frequency distribution onto light instead of sound.
It has to do with the power of the signal at different frequencies. White noise is "pure" noise in the sense that it has an equal power at all frequencies. Other colors of noise have different power distributions: blue noise has a power that grows linearly with the frequency, pink noise has a power that's inversely proportional to frequency, etc. The color names come from what you get if you map the same power/frequency distribution onto light instead of sound.