I realize the general compartmentalization of apps & services into spaces so you can control access and such.
But I am not clear on why there is also the concept of organization? Are usage charges done per org? Or is it just a way to organize spaces?
Organizations are the concept to manage resources and, well, organize work. The Cloud Foundry docs say about an organization:
An org is a development account that an individual or multiple collaborators can own and use. All collaborators access an org with user accounts. Collaborators in an org share a resource quota plan, applications, services availability, and custom domains.
As you said, spaces are used to deploy resources and to control access. Adding another org would make sense to introduce another department, project or maybe even a business unit to a Cloud Foundry instance like the IBM Cloud with Bluemix. Who is accountable (for the deployed resources)? How are projects and teams organized?