Transparent, understandable, and persuasive recommendations support the electricity consumers' behavioral change to tackle the energy efficiency problem. This paper proposes an explainable multi-agent recommendation system for load shifting for household appliances. First, we extend a novel multi-agent approach by designing and implementing an Explainability Agent that provides explainable recommendations for optimal appliance scheduling in a textual and visual manner. Second, we enhance the predictive capacity of other agents by including weather data and applying state-of-the-art models (i.e., k-nearest-neighbors, extreme gradient boosting, adaptive boosting, Random Forest, logistic regression, and explainable boosting machines). Since we want to help the user understand a single recommendation, we focus on local explainability approaches. In particular, we apply post-model approaches local, interpretable, model-agnostic explanation and SHapley Additive exPlanations as model-agnostic tools that can explain the predictions of the chosen classifiers. We further provide an overview of the predictive and explainability performance. Our results show a substantial improvement in the performance of the multi-agent system while at the same time opening up the "black box" of recommendations. Impact Statement This application paper addresses the explainability side of the load-shifting recommendations aiming at energy efficiency in residential households. Seeing the transparent and understandable recommendations daily will increase the awareness of residents of their energy consumption and will encourage more climate-related actions (supporting SDG 13). The shifted load will facilitate energy efficiency in the grid (SDG 7), foster energy innovation toward sustainable development (SDG 9), reduce the environmental impact, and stronger the households' sustainability, making them inclusive, safe, and resilient (SDG 11).