Pottery and ceramics are used as identifiers by archeologists for historic and prehistoric material cultures. They were widespread in use from the Neolithic to the Roman Empire - approximately ten thousand years and our imagination of Classical Civilizations such as Rome, Greece, Egypt and Mesopotamia wouldn't be complete without them. So why did they decline - if they did at all and if so, what replaced them?
'It didn't' is the simple answer - I'm not sure what your question is based on. Medieval ceramics absolutely exist, and indeed you dig through (literally) tonnes of them to get down to many Classical sites.
It is true that there is less in the way of widely-traded, recognisable styles like red-figure, black gloss and terra sigillata in Europe during the Early Middle Ages, but that is largely a function of shifting trade horizons and more things being done locally than at long distance - people still used pots, but they tended to be made fairly locally and so in a range of diverse styles. There was not much alternative - metal was expensive (and so metal vessels were a prestige good of the sort you might be buried with), glass even more so, and at any rate it was only really made in the Near East and North Africa until about the 12th century, when the Venetians picked up the art. The raw material for pottery, on the other hand, can be found all over the place and making it into ceramics is simply a matter of shaping it (which need not be done on a wheel) and sticking it in a kiln, which can again be made fairly simply. So if you wanted to cook something, store something, eat something or drink something, you were going to use pottery to do that.
There was a good AMA yesterday from two archaeologists working on medieval Tintagel, in Cornwall - this question and its answers helps you to see both what changed after the end of the Roman Empire and also the extent to which things didn't, at least at this one well-connected site.