Interpretability for machine learning models in medical imaging (MLMI) is an important direction of research. However, there is a general sense of murkiness in what interpretability means. Why does the need for interpretability in MLMI arise? What goals does one actually seek to address when interpretability is needed? To answer these questions, we identify a need to formalize the goals and elements of interpretability in MLMI. By reasoning about real-world tasks and goals common in both medical image analysis and its intersection with machine learning, we identify four core elements of interpretability: localization, visual recognizability, physical attribution, and transparency. Overall, this paper formalizes interpretability needs in the context of medical imaging, and our applied perspective clarifies concrete MLMI-specific goals and considerations in order to guide method design and improve real-world usage. Our goal is to provide practical and didactic information for model designers and practitioners, inspire developers of models in the medical imaging field to reason more deeply about what interpretability is achieving, and suggest future directions of interpretability research.