The purpose of Procrustes analysis is to fit one MDS solution (configuration, map), B, to another one, A, and eliminate superficial differences between B and A, by means of rotating, mirror-reflecting, dilating/magnifying, shrinking, or shifting/moving B, without changing either's shape.
Application 1. A is the physical location map, whereas B is the travel-time map produced by MDS. In Procrustes analysis, we fit B to A, which allows us to display B on the top of A and to spot differences.
Application 2. Y is easy to interpret, whereas the initial X is not. In Procrustes analysis, we fit X to Y in order to interpret X.
Application 3. F is the result from the female participants, whereas M is that from the male participants. In Procrustes analysis, we fit M to F (or F to M) so that we can compare the results from males and females on the same page (provided that the fitting is satisfactory).
Application 4. CH is is the result from Chinese participants, whereas AM is that from American participants. In Procrustes analysis, we fit CH to AM (or AM to CH) so that we can compare the cross-cultural results on the same page (provided that the fitting is satisfactory).