In fashion recommender systems, each product usually consists of multiple semantic attributes (e.g., sleeves, collar, etc). When making cloth decisions, people usually show preferences for different semantic attributes (e.g., the clothes with v-neck collar). Nevertheless, most previous fashion recommendation models comprehend the clothing images with a global content representation and lack detailed understanding of users' semantic preferences, which usually leads to inferior recommendation performance. To bridge this gap, we propose a novel Semantic Attribute Explainable Recommender System (SAERS). Specifically, we first introduce a fine-grained interpretable semantic space. We then develop a Semantic Extraction Network (SEN) and Fine-grained Preferences Attention (FPA) module to project users and items into this space, respectively. With SAERS, we are capable of not only providing cloth recommendations for users, but also explaining the reason why we recommend the cloth through intuitive visual attribute semantic highlights in a personalized manner. Extensive experiments conducted on real-world datasets clearly demonstrate the effectiveness of our approach compared with the state-of-the-art methods.