Red noise is a term for randomness in signals that is not totally uncorrelated (e.g., white noise) but has a particular frequency distribution with more of the lower frequencies (so-named because the color red comprises the lower frequencies of visible light). It is also called Brown noise or Brownian noise because Brownian motion matches it.
The term is used in discussion of signal detection. One example is the detection of extra-solar planets through astrometry, for which measurement noise is due to equipment and atmospheric anomalies.
For random noise with some other frequency distributions, the analogous terms pink noise, blue noise, and violet noise are used.