Sunspots are regions of much higher magnetic field, and lower temperature, on the surface of the sun. They occur in an eleven year cycle, and effect our planet through the solar wind.
When things are at different temperatures they emit different wavelengths of light, for example a piece of steel will pass through a number of colours as it is heated. The same is true of stars, and of the entire electromagnetic spectrum (not just visible light). We can use this fact to determine the temperature of the star.
The Hertzsprung-Russell (HR) diagram is a scatter plot of star magnitude against star brightness (there are other equivalent axes which are also used). It is a very useful way of grouping stars and plotting their evolution.