The WITH clause in PostgreSQL lets you define temporary named queries called Common Table Expressions (CTEs). These CTEs run first and create temporary result sets. Then the main query uses these results to produce the final output. For example, you can define a CTE named recent_orders that selects orders after a certain date. The main query then selects all rows from recent_orders. Execution starts by running the CTE, storing its results temporarily, then the main query runs using that temporary data. This helps break complex queries into simpler parts and reuse intermediate results. The execution table shows each step: starting the query, running the CTE, running the main query, returning results, and ending. Variables like recent_orders hold the temporary data after the CTE runs. Understanding that the CTE runs before the main query is key to using WITH clauses effectively.