Compound queries in Elasticsearch combine multiple conditions to filter documents. They use logical operators like AND (must), OR (should), and NOT (must_not). For example, a query with 'must' conditions requires all conditions to be true for a document to match. In the sample query, documents must have a title containing 'python' and a year greater or equal to 2020. The execution table shows step-by-step evaluation: first checking each condition per document, then combining results with AND. Document A matches both conditions and is included. Document B fails the title condition and is excluded. Changing 'must' to 'should' would include documents matching any condition. This approach helps build precise searches by combining multiple filters.