A cathedral is any church where a bishop has his headquarters. No matter how big a church is, if there's no bishop working in it, then it's not a cathedral. For instance, the cathedral of Laon in northern France lost its bishop when the town got smaller, and now it is only a church. And the church of Toulouse, even though it is a big beautiful church, never had a bishop, so it was never a cathedral. But most really big medieval churches in Europe are cathedrals.
Most famous medieval cathedrals are in Europe (where the Christians were), and they were built between about 1000 and 1600 AD. There are cathedrals all over Europe, in Spain, in England, in France, in Germany, and in Italy.
The architecture of cathedrals is based on the old Roman basilica. The earliest Christian churches were a lot like Roman basilicas. But cathedrals are bigger and higher than the biggest Roman basilicas. The earliest medieval cathedrals were built in the Romanesque style, and the later ones (beginning about 1100 AD) were built in the Gothic style. You'll find some examples of Romanesque and Gothic cathedrals on the Romanesque and Gothic pages.
Cathedrals were where Christian people in medieval Europe went to pray to God, and also where they took communion and talked to their priests. People also went to cathedrals to get married, or for baptisms or funerals. In the Middle Ages, most cathedrals did not have chairs in them, as they do today, and people stood or walked around during the Mass, or knelt on the stone floor to pray.
But cathedrals were not only for religious ceremonies. When bishops or lords or kings had important things to say to a group of people, they met in the cathedral, which was the biggest place in town that was inside, out of the cold and rain. If it was cold, many towns held their farmer's market inside the cathedral, and people also gathered there for safety if their town was being attacked.
To find out more about cathedrals, check out this book from Amazon or from your local library:
Cathedral: The Story of Its Construction, by David Macaulay (1981). Beautiful drawings and clear text explain exactly how medieval craftsmen built a cathedral, from foundation to the stained glass windows. For kids.