We don't know exactly. During the 1600's, there were no sun spot cycles observed, and Europe was in the grip of what climatologists call the Little Ice Age. Since 1700, there have been more or less regular cycles of typical length 11 years. Careful measurements of the luminosity of the Sun from satellite observations have shown that, when sun spots are present, the Sun is actually brighter, even though the spots themselves are dark! Surrounding regions of the solar surface become slightly brighter and in fact over compensate for the loss of luminosity by the sun spots. But this modulation of the solar output by sun spots produces only a 0.04 percent change in the solar constant, so it is very hard to believe that it has any direct affect upon earth weather. Some studies have suggested that the average ocean temperature increases and decreases, world-wide, by 0.5 degrees C in phase with the sun spot cycle, but the mechanism is not understood.
This entire subject is still under heavy investigation, because logically, any changes on the sun ought to have some level of climatic impact. Its just that there are so many other 'cycles within cycles' on the Earth, that solar effects, if they exist at all, are badly hidden.
All answers are provided by Dr. Sten Odenwald (Raytheon STX) for the
NASA IMAGE/POETRY project.