In the field of visual affordance learning, previous methods mainly used abundant images or videos that delineate human behavior patterns to identify action possibility regions for object manipulation, with a variety of applications in robotic tasks. However, they encounter a main challenge of action ambiguity, illustrated by the vagueness like whether to beat or carry a drum, and the complexities involved in processing intricate scenes. Moreover, it is important for human intervention to rectify robot errors in time. To address these issues, we introduce Self-Explainable Affordance learning (SEA) with embodied caption. This innovation enables robots to articulate their intentions and bridge the gap between explainable vision-language caption and visual affordance learning. Due to a lack of appropriate dataset, we unveil a pioneering dataset and metrics tailored for this task, which integrates images, heatmaps, and embodied captions. Furthermore, we propose a novel model to effectively combine affordance grounding with self-explanation in a simple but efficient manner. Extensive quantitative and qualitative experiments demonstrate our method's effectiveness.