A DO block in PostgreSQL lets you run anonymous procedural code without creating a stored function. It starts by optionally declaring variables, then executes procedural statements like printing messages or updating data. The example shows a DO block printing 'Hello, world!' as a notice. The execution table traces entering the block, executing the print statement, and finishing the block. Variables can be declared inside the block but are optional. The DO block does not return rows like a SELECT query; it is for side effects. This visual helps beginners see each step the database takes when running a DO block.