The theory is that sunspots protect the earth from gamma rays, and gamma rays are conducive to cloud formation and therefore sunspots reduce cloud cover.
There's be quite a competitive debate over the base 4 years or so about this, especially between Denmark's Henrik Svensmark and British Mike Lockwood. One thing that came out of the debate is that if Svensmark is directionally correct, he initially over-stated the magnitude of overall temperature change due to sunspots. Svensmark finally clarified in 2009 that sunspots have had zero overall contribution to global warming, and that the year-to-year variations can be see only after applying a linear rate of global warming of 0.14 degrees per decade. To the degree that Svensmark is correct, the solar minimum has been masking a small portion of global warming over the past couple of years and will contribute to a warming peak in 2013.
Lockwood on the other hand has theorized that sunspots affect annual regional weather rather than global temperatures. His work has shown that solar activity correlates strongly with weather in England and northern Europe.
