The short answer is, the ENERGY of a quake goes up by a factor of 31.6 for each factor of 1 on the Richter scale. USGS site has detailed explanations of this scale (and others).
Charles Richter developed the first "scale" meant to quantify the energy released by earthquakes. His work was done in the Bay Area of California, and as such, is really only useful when recording in this geologic domain. There are many factors that influence the energy released and how the energy is felt, so numerous scales are used now. One thing you should be aware of is that scientists no longer use the Richter scale. Instead, they use a number of different scales depending on what kind of motion they are wanting to detect. The scale that is usually reported to the public now is the Ml or Local Magnitude — this is close enough to the old scale that they don't bother to explain that it really isn't Richter any more.
