Most boat engines are cooled, directly or through a heat exchanger, by the water the boat floats in. A small pump with a flexible rubber impeller draws it in and pushes it round. On an outboard the pump sits in the lower unit, under the waterline. On an inboard it's on the engine, fed through a seacock and strainer.
The rubber vanes wear and take a set. BoatUS notes most owners have no idea when their outboard's pump was last serviced, and some don't know there is one. When it fails, the engine overheats.
What a surveyor checks
On an outboard, watch the tell-tale stream with the engine running: it should be steady. On an inboard, check water flow at the exhaust. Note the temperature gauge and any overheat alarm on the sea trial. Ask for the service record. If the pump is opened, look for cracked or missing vanes: BoatUS's photos show old vanes bent into a set beside straight new ones.
In the report
"Outboard, tell-tale stream weak and intermittent at idle, no record of impeller service. Replace the impeller and check the tell-tale passage before further use." See outboard water pump impeller.