A central challenge in the development of nanophotonic structures is identifying the optimal design for a target functionality, and understanding the physical mechanisms that enable the optimized device's capabilities. Previously investigated design methods for nanophotonic structures, including both conventional optimization approaches as well as nascent machine learning (ML) strategies, have made progress, yet they remain 'black boxes' that lack explanations for their predictions. Here we demonstrate that convolutional neural networks (CNN) trained to predict the electromagnetic response of classes of metal-dielectric-metal metamaterials, including complex freeform designs, can be explained to reveal deeper insights into the underlying physics of nanophotonic structures. Using an explainable AI (XAI) approach, we show that we can identify the importance of specific spatial regions of a nanophotonic structure for the presence or lack of an absorption peak. Our results highlight that ML strategies can be used for physics discovery, as well as design optimization, in optics and photonics.