Where the propeller shaft passes through the hull there's a hole to the sea. A traditional stuffing box closes it with packing that drips a little to stay cool. A dripless seal closes it with two faces pressed together: a carbon or graphite collar fixed to the boat and a stainless collar clamped on the shaft, held together by rubber bellows. It should stay dry.
Both kinds sit on the shaft log hose, a short rubber hose clamped to the hull's tube, and that hose is part of the check.
What a surveyor checks
Look for water at the seal with the shaft still and, on the sea trial, with it turning. It should be dry. Check the bellows for cracks, swelling or hardening, and ask for the service record: Practical Sailor notes these seals still have scheduled maintenance. Then the hose and clamps. Practical Sailor says to check the hose for age deterioration and corroded clamps, and calls double clamping essential.
In the report
"Shaft seal, dripless type, dry under way, bellows show surface cracking at the folds, no service record. Single clamps on the shaft log hose. Replace the bellows to the maker's schedule and double clamp the hose." See leaking shaft seal.