A teachable moment is an unplanned opportunity that arises in everyday life where the educator or holder of knowledge has a chance to give a valuable lesson to another person or group. Unlike traditional, structured learning experiences, a teachable moment is spontaneous and leverages a current situation or event to impart valuable lessons or concepts.
A striking example is a cancer diagnosis, which is considered a teachable moment to induce smoking cessation.
In the context of a medical diagnosis, a failed exam, or other emotional setting a teachable moment refers to the heightened state of awareness and readiness to change. The reality of facing a serious health condition, or the shame of failing an exam can bring a sudden and stark clarity, prompting individuals to reflect on their health and lifestyle choices or learning habits more deeply than they might have previously.
A related scientific article can be read here.