"Solar max" is a time when there are lots of sunspots. The picture on the left shows the Sun near solar min in 2001. A few years later the Sun moved into the "solar min" phase of the sunspot cycle... a time when there are very few sunspots. That solar min was quite odd. There were hardly any sunspots for several years. There aren't any sunspots in the picture on the right, which was taken in 2009.
Images courtesy of SOHO/NASA/ESA.