The inversability message indicates the percentage of the new grid data that matches the original grid, after the new grid is projected back into the original projection.
Although changing from one projection
to another is accomplished with a single command, it is actually a two-step
process. The first step changes the projection of the data from what it was
stored in to geographic coordinates on a sphere or spheroid. This is referred
to as 'inversing the projection.' The next step changes it to the desired output
projection. This is referred to as the 'forward transformation' of the projection, which involves resampling of the new grid.
After a forward transformation, ArcInfo reprojects the new grid into its original projection. Center points of cells within the new grid can be shifted due to the distortion inherent to a particular projection. When the new grid is reprojected back into the original projection, those center points may not be projected exactly on or near their original position (usually the difference is minimal). Hence the inversability percentage message.