Describing and forecasting city traffic is challenging, given the array of factors influencing the movement of pedestrians and vehicles. Faced with this complexity, research has focused on machine learning as a way to capture spatio-temporal traffic patterns, based on past sensor data. While the methods can accurately forecast high-dimensional observations, it is often hard to explain the models and their predictions. In many cases, only the predictive performance of an otherwise black box model is evaluated. An accurate but explainable alternative is provided by the Koopman operator, an emerging methodology for data-driven identification of high-dimensional and nonlinear dynamical systems. In this study, we showcase the method by analyzing pedestrian traffic data from Melbourne, Australia. We formulate our computations in the Extended Dynamic Mode Decomposition framework, where we approximate the Koopman operator in a function basis computed with time delay embedding and the Diffusion Map algorithm. The model captures the distinct temporal patterns of 11 traffic sensors simultaneously. Because the dynamics become linear in the operator-theoretic perspective, we can decompose the model into its spectral components. Importantly, these components facilitate interpretation and can increase scientific understanding of the underlying system and the model’s operations. For the Melbourne data, we show that the spectral components connect to the underlying state space geometry and indicate the model’s stability over a prediction horizon. Our study showcases how the Koopman operator framework offers explainable and accurate data-driven predictions in a real-world traffic system. The results can easily be transferred to other traffic systems.