Network alignment (NA) identifies corresponding nodes across multiple networks, with applications in domains like social networks, co-authorship, and biology. Despite advances in alignment models, their interpretability remains limited, making it difficult to understand alignment decisions and posing challenges in building trust, particularly in high-stakes domains. To address this, we introduce NAEx, a plug-and-play, model-agnostic framework that explains alignment models by identifying key subgraphs and features influencing predictions. NAEx addresses the key challenge of preserving the joint cross-network dependencies on alignment decisions by: (1) jointly parameterizing graph structures and feature spaces through learnable edge and feature masks, and (2) introducing an optimization objective that ensures explanations are both faithful to the original predictions and enable meaningful comparisons of structural and feature-based similarities between networks. NAEx is an inductive framework that efficiently generates NA explanations for previously unseen data. We introduce evaluation metrics tailored to alignment explainability and demonstrate NAEx's effectiveness and efficiency on benchmark datasets by integrating it with four representative NA models.