The stuffing box sits on the inside end of the shaft log, the tube where the propeller shaft leaves the hull. A short hose clamps it to the log. Inside, rings of greased packing squeeze round the shaft, and a nut compresses them.
It's meant to drip. Practical Sailor puts a healthy one at 3 to 4 drips a minute underway. Good Old Boat's test is touch: after a long run it should feel warm, never hot. Many boats now have a dripless seal in its place, which stays dry but still has a maker's service schedule.
What a surveyor checks
The drip rate with the shaft turning and with it still. Heat after the sea trial. The shaft log hose for cracks and softness, and its clamps: Practical Sailor calls double clamping essential, because that hose is all that stands between the sea and the boat at the shaft.
In the report
"Stuffing box dripping about 12 a minute underway and continuing with the shaft stopped. Adjust or repack, and double clamp the shaft log hose." See leaking shaft seal.