Data mining- Clustering techniques
It's common to perform clustering on certain features, and then use characteristics such as mean differences between other features (not used in clustering) to show how clusters differ.  It's not always meaningful to say that clusters differ merely by lower distances between cluster centers and objects assigned to them (as in k-means).

As an example, you might acquire other features (variables) for the states and then average each feature among objects assigned to each cluster.  Then show bar charts of averages for those variables among all the clusters to assist in explaining how the clusters differ.  You might also test for significantly different means of the supplemental features across clusters.