Explainable recommendation is far from being well solved partly due to three challenges. The first is the personalization of preference learning, which requires that different items/users have different contributions to the learning of user preference or item quality. The second one is dynamic explanation, which is crucial for the timeliness of recommendation explanations. The last one is the granularity of explanations. In practice, aspect-level explanations are more persuasive than item-level or user-level ones. In this paper, to address these challenges simultaneously, we propose a novel model called Hybrid Deep Embedding (HDE) for aspect-based explainable recommendations, which can make recommendations with dynamic aspect-level explanations. The main idea of HDE is to learn the dynamic embeddings of users and items for rating prediction and the dynamic latent aspect preference/quality vectors for the generation of aspect-level explanations, through fusion of the dynamic implicit feedbacks extracted from reviews and the attentive user-item interactions. Particularly, as the aspect preference/quality of users/items is learned automatically, HDE is able to capture the impact of aspects that are not mentioned in reviews of a user or an item. The extensive experiments conducted on real datasets verify the recommending performance and explainability of HDE. The source code of our work is available at \url{https://github.com/lola63/HDE-Python}