Smart home environments are designed to provide services that help improve the quality of life for the occupant via a variety of sensors and actuators installed throughout the space. Many automated actions taken by a smart home are governed by the output of an underlying activity recognition system. However, activity recognition systems may not be perfectly accurate and therefore inconsistencies in smart home operations can lead users reliant on smart home predictions to wonder "why did the smart home do that?" In this work, we build on insights from Explainable Artificial Intelligence (XAI) techniques and introduce an explainable activity recognition framework in which we leverage leading XAI methods to generate natural language explanations that explain what about an activity led to the given classification. Within the context of remote caregiver monitoring, we perform a two-step evaluation: (a) utilize ML experts to assess the sensibility of explanations, and (b) recruit non-experts in two user remote caregiver monitoring scenarios, synchronous and asynchronous, to assess the effectiveness of explanations generated via our framework. Our results show that the XAI approach, SHAP, has a 92% success rate in generating sensible explanations. Moreover, in 83% of sampled scenarios users preferred natural language explanations over a simple activity label, underscoring the need for explainable activity recognition systems. Finally, we show that explanations generated by some XAI methods can lead users to lose confidence in the accuracy of the underlying activity recognition model. We make a recommendation regarding which existing XAI method leads to the best performance in the domain of smart home automation, and discuss a range of topics for future work to further improve explainable activity recognition.