Amateur radio has no single governing body. What it has is a layered set of organizations: treaty bodies that divide the spectrum, national regulators that write the rules, national societies that represent operators, and specialty groups that run satellites, exams, awards and repeaters. In the United States exactly one of them can tell you what you may transmit — the FCC, in Part 97. Everything else, from band plans to contest rules, is voluntary coordination that works because operators choose to follow it.
Membership organizations do three things an individual operator cannot: represent the service to regulators, maintain shared infrastructure such as question pools, award programs, repeater coordination and satellites, and train the next operators.
Related topics: clubs and community for the local layer, where most of the actual work happens, and amateur radio history for how these bodies came to exist.