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I think that Galaxy Optics (a highly respected US mirror maker) definition of RMS wavefront error gives more than enough explanation that should satisfy most amateur astronomers and what they are hoping to achieve.
Quote from the Galaxy Optics website-
"RMS Wavefront Error:
RMS wavefront error is a statistical measure of how much a mirror's wavefront deviates from the ideal theoretical wavefront. The RMS wavefront error is calculated from all of the measured interferometric data points and is the best indication of a mirror's overall performance. To obtain the RMS value the fringe analysis software measures all of the data points to determine the error between the point positions on a theoretically perfect wavefront and their actual positions on the wavefront under test. The deviation between points is squared then averaged and the square root is extracted. The literature states and physical tests prove that an optic with a RMS wavefront value of 0.076 or less is diffraction limited."
PeterM.
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