If you look at this piece of pottery, you will see that it is a deep red, and looks as though it has been polished. In fact, it was made without any polishing. What the Romans discovered was how to make a very wet, almost sloppy, clay that would eventually look as though it were polished after simply putting it into an oven (kiln) to bake it.
This kind of pottery was made into dishes, bowls and serving plates with the same designs, so was all a matching set.
They all used moulds of plaster, which had the designs stamped into their insides. The bowl and plates you see are castings. They have not been turned on a potter's wheel. They used an open design, so that, as the wet pottery dried naturally, it shrank away from the mould and could be pulled out without breaking the mould. The use of plaster for moulds was important. Plaster soaks up water, so the clay touching the mould dries out.
They took some expertise to make. The clay is not thick, as we might imagine with normal pottery shaped on a wheel. It is runny. It is poured into the mould, the water in the clay allowed to soak out through the plaster. The inside of the mould still contained runny clay. When it was judged that the surface touching the mould had dried to be thick enough, the surplus clay was poured out, leaving a bowl or plate behind.