pink~ generates pink noise, as distinguished from white noise (which the MSP object noise~ generates). White noise has constant spectral power per hertz of bandwidth, while pink noise has constant power per octave. Subjectively, pink noise sounds less hissy than white noise.
The pink~ object generates a signal consisting of random value in the range -1.0 to 1.0, with an even distribution of power per octave of frequency. Noise with this power distribution is known as "pink noise". "White noise", as generated by the object noise~, has an even distribution of power over all frequencies. Perceptually, white noise sounds bright and harsh, and pink noise sounds more even and "natural".
pink~ generates random numbers such that the frequency content is equal power per octave