Terminus post quem is an archaeological term used to describe a situation where something is later than a certain date.
For example: if you found a coin dating to 1915 in a pit in your garden, then the pit would have to have been dug in or after 1915. The "or after" is important: if you only find one coin in the pit, you cannot tell if the pit was dug in 1915, 1916, 1960, or any time after 1915, and the coin dropped in.
The phrase terminus post quem is therefore very important to archaeologists. In the Great Yarmouth Archaeological Map, all finds are termini post quem. There is no way of telling whether a 12th century pot was put there in the 12th century, or in the 14th century.
When a number of objects are recovered from one deposit, the terminus post quem is determined by the youngest object: all the other finds, even though they are older, were put there at the same time, so the deposit must be younger than the youngest object.
The opposite of a terminus post quem is a terminus ante quem, where a deposit must have been laid before a certain date. These are fairly rare in archaeology. However, the eruption of Pompeii in AD79 formed a terminus ante quem for the city: everything under the lava must have been there before AD79.