Existing recommender systems in the e-commerce domain primarily focus on generating a set of relevant items as recommendations; however, few existing systems utilize underlying item attributes as a key organizing principle in presenting recommendations to users. Mining important attributes of items from customer perspectives and presenting them along with item sets as recommendations can provide users more explainability and help them make better purchase decision. In this work, we generalize the attribute-aware item-set recommendation problem, and develop a new approach to generate sets of items (recommendations) with corresponding important attributes (explanations) that can best justify why the items are recommended to users. In particular, we propose a system that learns important attributes from historical user behavior to derive item set recommendations, so that an organized view of recommendations and their attribute-driven explanations can help users more easily understand how the recommendations relate to their preferences. Our approach is geared towards real world scenarios: we expect a solution to be scalable to billions of items, and be able to learn item and attribute relevance automatically from user behavior without human annotations. To this end, we propose a multi-step learning-based framework called Extract-Expect-Explain (EX3), which is able to adaptively select recommended items and important attributes for users. We experiment on a large-scale real-world benchmark and the results show that our model outperforms state-of-the-art baselines by an 11.35% increase on NDCG with adaptive explainability for item set recommendation.