Interpretation Result of K means Algorithm

In clustering, the goal is usually to get high similarity within each group, and low similarity between each group. Let's translate it to statistical terms: high similarity within a group low variance within the cluster, or within_SS. Now, let's say you compute all the variance in the data, and call it total_SS. In optimal clustering, since the clusters are very different from each other, then most of the total variance is explained by the variance between the groups. And of course, since the variance within each group is very small, it would explain only a small fraction of the total variance in the data.