Knowledge distillation (KD) improves the performance of a low-complexity student model with the help of a more powerful teacher. The teacher in KD is a black-box model, imparting knowledge to the student only through its predictions. This limits the amount of transferred knowledge. In this work, we introduce a novel Knowledge Explaining Distillation (KED) framework, which allows the student to learn not only from the teacher's predictions but also from the teacher's explanations. We propose a class of superfeature-explaining teachers that provide explanation over groups of features, along with the corresponding student model. We also present a method for constructing the superfeatures. We then extend KED to reduce complexity in convolutional neural networks, to allow augmentation with hidden-representation distillation methods, and to work with a limited amount of training data using chimeric sets. Our experiments over a variety of datasets show that KED students can substantially outperform KD students of similar complexity.