Hash partitioning in PostgreSQL works by computing a hash value of the partition key for each row. Then, the system calculates the modulo of this hash by the number of partitions to find which partition the row belongs to. For example, if there are 4 partitions, the modulo is hash % 4, resulting in a number from 0 to 3. Each number corresponds to a partition. Rows with the same key always go to the same partition because the hash is consistent. This method helps distribute data evenly across partitions. If the number of partitions changes, the modulo divisor changes, which can cause rows to move to different partitions. The execution table shows step-by-step how rows with different region values are assigned to partitions based on their hash and modulo results.