Nautical term: an exposed partial stern deck
'Poop' is just one of those English words which fascinate. The use of the word in this expression derives from Mediterranean sailing ships, whose superstitious crews would not sail without a small image of some god on board the vessel. The ancient Phoenician and Greek sailors believed that there was a need to protect this image from the elements, so that the god would provide them with safe journeys in return. This led to the construction of a raised deck at the stern of the ship, beneath which the idol would be placed and given a shrine. The Romans referred to the idols as 'puppim' (from the Latin for a small image or doll, from which we also derive the words 'puppet' and 'poppet'). Medieval English sailors referred to this shelter as the 'poupe', and the expression stuck.
The poop deck also became a gathering place for sailors in their off-duty hours, and hence was the source of much gossip and inside information, and the word 'poop' is often used to refer to the latter (scuttlebutt being the preferred nautical term for gossip).
In later years, the area below the poop deck was also used for accomodation, bunk space and cabins being built under it. If the weather became sufficiently harsh, waves might break over the deck, at which point, the ship was said to be pooped, and the flooding would render the ship more difficult to steer. This possibly led to the modern use of the expression to mean "tired", as the ship seems to respond more slowly.
There was an upside though - the poop deck in vessels such as the medieval carevelle, which had a high poop deck, gave it a maneuvering advantage under some circumstances, as it was easier to steer into the wind (and waves).
Modern vessels preserve the word, and the poop deck remains. In these slightly less superstitious times, it more frequently provides accommodation for the crew, and in heavy weather, prayers to chosen deities are doubtless still offered.