Imagine a doctor treating a patient. She listens to what the patient says, probing for more information, then makes some direct observations, asking if it hurts when she presses here, listening to breathing, etc, before making some treatment recommendations. Imagine another doctor who never actual meets his patient, but just semds them for blood tests, looks over the results and assumes everything is fine. Which doctor would be more effective at maintaining healthy patients?
Well run agile projects regularly take time to inspect the actual product being produced and judge the health of that product directly. Waterfall projects tend to look at secondary artefacts to give clues (or reassurance) about the health of the product – normally these are adherence to milestones in a plan and to budget constraints. In fact waterfall focuses very much on the project rather than on the product and the terminology reflects this – project plans and project managers vs product backlogs and product owners.
Of course good project managers on waterfall projects instinctively know how their product is looking and will take corrective action if required though there is nothing in the 'methodology to force them to'. However, many ‘green’ PMs are genuinely astonished at the end of the project to find the product doesn’t stack up with users. ‘But everything has gone to plan and we are under budget – I don’t understand what went wrong’.
In summary, agile measures health of the Product, waterfall measures health of the Project, these are different things.