Identify significant features in clustering results
A similar post appears on Cross-Validated, &quot;Estimating the most important features in a k-means cluster partition&quot;.
Quoting from that post:

One way to quantify the usefulness of each feature (= variable =
dimension), from the book Burns, Robert P., and Richard Burns.
Business research methods and statistics using SPSS. Sage, 2008.
(mirror), usefulness being defined by the features'
discriminative power to tell clusters apart.

We usually examine the means for each cluster on each dimension using
ANOVA to assess how distinct our clusters are. Ideally, we would
obtain significantly different means for most, if not all dimensions,
used in the analysis. The magnitude of the F values performed on each
dimension is an indication of how well the respective dimension
discriminates between clusters.

Another way would be to remove a specific feature and see how this
impact internal quality indices. Unlike the first solution, you
would have to redo the clustering for each feature (or set of
features) you want to analyze.
FYI:

Can a useless feature negatively impact the clustering?
Can the choice of the measurement units of the features impact the clustering?
Why vector normalization can improve the accuracy of clustering and classification?
What are the most commonly used ways to perform feature selection for k-means clustering?


Furthermore, there is a paper on Feature Selection in Clustering Problems

A novel approach to combining clustering and feature selection is
presented.   It  implements  a wrapper strategy  for  feature
selection,  in  the sense that the features are directly selected by
optimizing the discriminative power of the used partitioning
algorithm.  On the technical side, we present  an  efficient
optimization  algorithm  with  guaranteed  local  convergence
property.  The only free parameter of this method is selected by a
resampling-based stability analysis.  Experiments with real-world
datasets demonstrate that our method is able to infer both meaningful
partitions and meaningful subsets of features.