So, TEM stands for Transverse Electromagnetic Mode. It describes the intensity pattern of the beam cross section, transverse, or perpendicular, to the direction of travel. The numbers tell you which mode the emitted light is. So for TEM00 you have a primary mode of the laser and its intensity pattern is more or less a 2-dimensional gaussian distribution, basically a single spot. Higher order modes such as TEM02 or TEM10, etc, have different patterns. Wikipedia has a few nice pictures to describe this visually.
http://en.wikipedia.org/wiki/Transverse_mode
http://en.wikipedia.org/wiki/Transverse_mode