What pink noise is
In white noise every frequency is equally loud. In pink noise loudness falls as frequency rises: each octave is 3 dB quieter than the one below. The highs are softened, so it sounds warmer.
It sounds like steady rain, wind in the trees or a distant waterfall. Many people find it easier than white noise for long listening.
Pink noise and sleep
Pink noise often comes up in articles about deep sleep. In studies (for example Papalambros et al., Frontiers in Human Neuroscience, 2017), short pulses of pink noise were timed to the brain's slow waves during sleep, and older participants' memory improved. That was precise lab stimulation, not background noise all night.
As background, pink noise works like any steady noise: it covers sharp sounds around you. If you like it, that's enough.
How to listen
Quietly, like rain outside the window. Keep the source away from your pillow. Set the timer for 30 to 60 minutes so it fades once you're asleep.