It may be a corporation or a company, a government agency, a family working on their farm, a volunteer association, or a union. An organization is different from a project team. Organizations are permanent, or at least intended to survive beyond a single project. A project team, on the other hand, is a temporary association of people who belong to different parts of an organization and agree to work together to achieve a specific deliverable. The project team disbands at the end of the project, while its members continue to work for their respective organizations.
Organizations exist within organizations.
The scope of the organization is a matter of perspective. If you are the C.E.O. of a multinational corporation, your scope may include numerous autonomous companies as well as corporate staff functions. If you are the president of a company within that conglomerate, the relevant organization is the entire company. If you are the I.S. executive within that company, the organization you care most about is the I.S. department. I.S. departments make excellent examples of organizations within an organization.