To facilitate the interpretation of the dimensions in the reduced space, we may do internal or external analyses.
In internal analysis, we use the same proximities data, run alternative analysis method (e.g., cluster analysis) with them, and embed the results within MDS. If different methods all converge to the same interpretation, then it is!
In external analysis ("property fitting"), we use supplementary data. Specifically, we may try to predict the property (collected on the objects) for object_i from the 2D coordinates for the objects through multiple regression.
For example, in a study, the objects are 14 stressful experiences relevant to early parenting, and the two dimensions are labeled as "major vs. minor child problems" and "child welfare vs. self-welfare". The external property is "infuriating", and we want to predict "infuriating" for each of the 14 objects from the 2D coordinates for the 14 objects, which results in a directed line. It is found that infuriating tends to be associated with the problems of self-ware as opposed to the welfare of the child.
In external analysis, we regress a given external attribute of the objects (e.g., "infuriating") on the 2D coordinates of the objects (i.e., dim 1 and dim 2), and the resulting unstandardized multiple regression coefficients form a point in the 2D space. A directed line is then drawn from the origin to that point. Evidently, the projections of the objects on this line give a set of 2D coordinates, (dim1, dim2), which correspond best to the external attribute (Borg & Gronen, 2005, pp.77-79).