Self-driving cars increasingly rely on deep neural networks to achieve human-like driving. However, the opacity of such black-box motion planners makes it challenging for the human behind the wheel to accurately anticipate when they will fail, with potentially catastrophic consequences. Here, we introduce concept-wrapper network (i.e., CW-Net), a method for explaining the behavior of black-box motion planners by grounding their reasoning in human-interpretable concepts. We deploy CW-Net on a real self-driving car and show that the resulting explanations refine the human driver's mental model of the car, allowing them to better predict its behavior and adjust their own behavior accordingly. Unlike previous work using toy domains or simulations, our study presents the first real-world demonstration of how to build authentic autonomous vehicles (AVs) that give interpretable, causally faithful explanations for their decisions, without sacrificing performance. We anticipate our method could be applied to other safety-critical systems with a human in the loop, such as autonomous drones and robotic surgeons. Overall, our study suggests a pathway to explainability for autonomous agents as a whole, which can help make them more transparent, their deployment safer, and their usage more ethical.