Red noise has two common definitions:
(1) Another name for brown noise.
(2) An oceanographic term which describes the ambient noise of distant underwater objects.
The "red" name reportedly refers to the loss of higher frequencies and the emphasis on lower frequencies (this is from the white noise / white light analogy). This would apply to either of the above definitions.
Red noise is not nearly as clearly defined as white or pink noise. Some definitions found on the web conflict with each other, for example, some sources define red noise as a synonym for pink noise.
Main page: Noise Colours