Tableware means all the things you put on a table for a meal: plates, bowls, cups, glasses, knives, forks, spoons, dishes for serving. It is a group word — one word that covers the whole set — so you almost never use it for one object. You would not point at a plate and call it 'a tableware'.

It has no plural and takes no 'a': you say 'the tableware', 'some tableware', 'a lot of tableware'. This is the same pattern as 'furniture' and 'luggage'.

Where you meet it: shops, catalogues, hotels, restaurants — the business side of eating. A department store will have a tableware floor. A restaurant manager will talk about buying new tableware. At home, ordinary people usually don't say it; they say 'the plates and things', 'the dishes', or name the thing directly. So it sounds a bit formal, a bit like the language of selling.

There are narrower words inside it. 'Crockery' is the pottery part (plates, cups, bowls). 'Cutlery' is the knives and forks — Americans often say 'silverware' or 'flatware'. 'Glassware' is the glasses. 'Tableware' is the umbrella over all of them.