In your own words, explain how changes in the number of sunspots is related to changes in global climate.

The sunspots are eruptions of heat and light energy emitting from the surface of the sun. These can increase our energy absorption many times above normal. Especially if it is pointed directly at the earth. These have been known to disrupt several bands in the radio spectrum and have knocked out communications of satellites. Naturally all this energy would have a great effect on our earth in many ways, climate included.

 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.