A summarizer that minimizes the KL divergence minimizes Redundancy while maximizing Relevance.
in fact, this is an instance of the Kullback Minimum Description Principle (MDi) (Kullback and Leibler, 1951), a generalization of the Maximum Entropy Principle (Jaynes, 1957): the summary minimizing the KL divergence is the least biased (i.e., least redundant or with highest entropy) summary matching D. this summary fits D while inducing a minimum amount of new information.