A gymnasium is a place people go to exercise or participate in sports. Your neighborhood gymnasium might be a good place to play basketball, pump iron, or to check out the other gym rats.
The more common gym is a shortened form of gymnasium. Most schools have a gymnasium, a room where physical education classes are held and games like dodge ball and volleyball can be played. People also belong to private gymnasiums, where they take yoga classes and run on treadmills and lift weights. In Latin, gymnasium means "school for gymnastics," from the Greek gymnasion, "public place where athletic exercises are practiced."