In this case, a wavefront can be thought of as a line which connects points possessing equal phases, (across multiple parallel propagating waves).
Wiki definition here.
The ideal mirror would produce equidistant phase alignments (ie parallel wavefronts), from an initially coherent light source.
Errors in the surface, would produce misalignment of these 'wavefronts' such that they would no longer be parallel (when viewed over time). If a perfectly parallel set of lines could be drawn representing an ideal set of 'wavefronts', you would find that the phases of the light intersecting these lines, (from an errored mirror surface) would not be the same. If different phases come together at any point, constructive or destructive interference results, varying the intensity and amplitude, which gives rise to fringe patterns.
Wavefront errors could be thought of as deviations in phase angle, of the light about a common (mean) value.
Hope this helps.
Cheers & Rgds