Character dances are dances from different countries, like Spanish dances, Hungarian Dances (Czardas for instance!), Russian folk dances, Irish dance, etc., etc. The Polish National Character dance is the Mazurka, for instance. All of these dances are great fun to learn and to perform, and in ballets they can be very important parts of the story by showing the dance of the people who lived in the time and place of the story, whether they are peasants or important court people.
If you look at videos of most of the full length ballets you will find several National Character Dances. In Swan Lake, for instance, there is a Mazurka and a Czardas. There is also a very famous and wonderful Mazurka in Coppelia.