Explaination or Description of clusters after clustering
It depends on the clustering technique you use. Since you tagged this post with k-means I will assume this is what you are using. Cluster centers should already be somewhat informative for laymans, but since you should be/are scaling this can lose some of it's interpretation. 

What you could do is assign class labels to each sample based on in what cluster they ended up in. Then you could fit a multi-class decision tree to your data and use the decision rules for interpretation, like 60% of cluster 1 has $x_1 &lt; 0.9$.