Unsupervised black-box models are drivers of scientific discovery, yet are difficult to interpret, as their output is often a multidimensional embedding rather than a well-defined target. While explainability for supervised learning uncovers how input features contribute to predictions, its unsupervised counterpart should relate input features to the structure of the learned embeddings. However, adaptations of supervised model explainability for unsupervised learning provide either single-sample or dataset-summary explanations, remaining too fine-grained or reductive to be meaningful, and cannot explain embeddings without mapping functions. To bridge this gap, we propose LAVA, a post-hoc model-agnostic method to explain local embedding organization through feature covariation in the original input data. LAVA explanations comprise modules, capturing local subpatterns of input feature correlation that reoccur globally across the embeddings. LAVA delivers stable explanations at a desired level of granularity, revealing domain-relevant patterns such as visual parts of images or disease signals in cellular processes, otherwise missed by existing methods.