Technically a ceramic is any inorganic, non-metallic, solid material that is created by heating and then cooling it, however to most people ceramics are associated with clay pottery. There is a good reason for this, the original ceramic materials where made out of clay and turned into pottery and tiles. Ceramics are one of the oldest materials known to man, they were first created by prehistoric man.
About twenty five thousand years ago prehistoric man discovered that if they mixed clay and water and then fired it in a kiln they could create solid objects that could shaped into whatever they happened to need. This worked out well for them because they needed some way to store food and water and ceramic pots proved an ideal solution. The ancient Egyptians took up pottery and advanced the art by a considerable degree, by building kilns that operated at much higher temperatures and by glazing there ceramics. The also discovered how to make glass, the first of the new types of ceramic.
After the Egyptians there really weren't any great advances in the field of ceramics until the industrial revolution. New technology made it possible to make newer types of ceramics and created new uses for them. Ceramics really took off in the twentieth century as all kinds of new ceramic materials and uses for them were discovered.
Ceramics are used in everything from spacecraft to computers as well as virtually every other high tech and low tech device. When we about exotic new materials being used to make better semiconductors or jet engines they are usually ceramics. Modern medical research has started to use ceramics extensively as a replacement for bone.
There are a lot of good reasons to use ceramics, the primary ones being that they are usually lighter and harder than steel, they are also much more resistant to heat than metals. Ceramics are often used in high temperature applications because they can withstand a much higher heat. The downside to ceramics is that the are also more brittle than steel and harder to manufacture. To a certain extent this has limited there use in things like car engines where they would be ideally suited, at the current time they just can't be made reliable enough.
Despite all of the high tech applications of ceramics they are still used in their more traditional roles. It is still possible to get ceramic dinnerware and ceramic tiles, in fact ceramic tiles are still the best option for most kitchens and bathrooms. Ceramic dinnerware is still often made of clay but most tiles are now made out of plastics that have been fired in a kiln. They are much more durable and they can be made in a wider variety of colours than clay ceramics.