The use of wearables in medicine and wellness, enabled by AI-based models, offers tremendous potential for real-time monitoring and interpretable event detection. Explainable AI (XAI) is required to assess what models have learned and build trust in model outputs, for patients, healthcare professionals, model developers, and domain experts alike. Explaining AI decisions made on time-series data recorded by wearables is especially challenging due to the data's complex nature and temporal dependencies. Too often, explainability using interpretable features leads to performance loss. We propose a novel XAI method that combines explanation spaces and concept-based explanations to explain AI predictions on time-series data. By using Inherently Interpretable Components (IICs), which encapsulate domain-specific, interpretable concepts within a custom explanation space, we preserve the performance of models trained on time series while achieving the interpretability of concept-based explanations based on extracted features. Furthermore, we define a domain-specific set of IICs for wearable-based health monitoring and demonstrate their usability in real applications, including state assessment and epileptic seizure detection.