Rotary International is, first and foremost, an organization of Rotary Clubs. It is Rotary clubs that belong to Rotary International, not individual Rotarians.  Individual Rotarians are members of their local Rotary clubs. Whether you are the president of Rotary International, or the most recent Rotary inductee, you are a member of a Rotary club, and not a member of Rotary International.
It is the purpose of Rotary International to support the work that Rotary clubs are doing. It is Rotarians, volunteering in their Rotary clubs, who come up with the project ideas, the fund-raising opportunities and the fellowship events. And it is Rotary International that supports them.
But how? With over 35,000 clubs and 1.2 million Rotarians, how is Rotary International able to support all of this? That is where the structure of Rotary comes in. Like any large, international organization, the challenge must be broken into bite-sized pieces. So it is with Rotary International. 
The Rotary world is divided into 34 zones, each with approximately the same number of Rotarians. Zones are paired together, and each pair of Zones, elects a director to serve a two-year term on the Rotary International Board of Directors, for a total of 17 directors. And each director is responsible to provide support to the districts within their zone.
Wait, you say, what is a district? A district is a group of about 60-80 Rotary Clubs that are organized based on geographical, linguistic, cultural and other characteristics that allow them to operate as a cohesive unit. Working out to about 540 districts worldwide, each district annually selects a district governor whom serves a single one-year term. It is the district governor and their district team that provides direct support to a Rotary club.
So, there you have a basic overview of the organizational infrastructure of Rotary International, with the Rotary clubs occupying the pivotal role, and the rest of Rotary International serving the Clubs.
Ken Parsons
District 5495, Area 9, Assistant Governor