There are several different kinds of governing bodies for sports:
International federations - these take care of one sport (or a group of sports, such as skiing). They create a common set of rules and organise international competitions. Promotion of the sport is also a task of an international federation.
National federation - these have the same objectives as an international federation, but then within the scope of one country, or even part of a country.
Multi-sport event organisers - these take care of the organisation of a certain event which contains more than one sport. The most important example is the IOC, organiser of the Olympic Games.
General sports organisations - these take care of sports related topics, usually for a certain group, such as Catholic or Jewish sport, military or university sport.
Professional leagues
The first international federations were formed at the end of the 19th century.