Fuzzy matching in Elasticsearch works by taking the input query term and generating similar variants based on allowed differences called fuzziness. The query then searches the index for these variants, calculates similarity scores for each match, and returns documents with scores above a threshold. For example, searching for 'roam' with fuzziness 'AUTO' generates variants like 'room' and 'foam'. Each variant is scored for similarity, and only close matches are returned. This helps find results even if the search term has typos or small differences. The process starts with receiving the query, generating variants, searching the index, scoring matches, filtering results, and finally returning the matched documents.