A sunspot equilibrium is a market equilibrium in which prices depend on otherwise irrelevant random variable. The name is inspired by a theory of nineteenth century economist William Jevons that sunspots affected the stock market. (The theory, while wrong, isn’t quite as rediculous as it sounds. Jevons thought, by looking at the data he had on sunspots and agricultural prices, that he detected a pattern that indicated that sunspots caused crops to fail, which in turn caused recessions.)
A sunspot equilibrium would then be a self-fulfilling prophecy. If everyone expected that sunspots caused recessions, that in principle could be sufficient to cause a recession, even if the cause-and-effect existed entirely in people’s heads. Note that this outcome, while not optimal, would still be individually rational: even if you knew that sunspots didn’t really cause recessions, you would know that everyone else was expecting a recession, so you would act accordingly.