The US boat rules define the transom as the surface at the stern of a boat, projecting or facing aft. On an outboard or sterndrive boat it's a structural part: the engine hangs on it or bolts through it, and it takes the thrust.
Many transoms are cored with plywood. Every fastening through it, from engine brackets to transducers, ladders and drain fittings, is a path for water into the wood. Soundings lists loose, badly fitted or badly bedded hardware as the way in.
What a surveyor checks
Sounding the transom in a grid. A wet core gives the deep "thup" Soundings describes, and the hammer doesn't bounce back as strongly. A moisture meter on dry gelcoat to map it. Dirty cracks and weeping round fittings. With the engine loaded or levered, any flex. On a sterndrive boat, the bellows and the transom from inside.
The HIN on a US boat is on the starboard side of the transom, near the top, so the surveyor reads it here too.
In the report
"Transom, starboard of the drive, area about 400 by 300 mm dull on sounding with high readings. No flex under load." See wet transom core.