Organizations are separate from your personal account and are best suited for businesses who need to manage permissions for members. You can use your personal account to login and manage your organization. You can even create more organizations with different plans and billing using the same account.
To add a member into your organization go to settings and enter their e-mail to send an invite. You can also set their account type to Developer or Designer. Users added from here will get access to all projects in your organization.
If you want to give the member access only to a specific project, go to that project you want to share and add them there.
Now if you go back to the settings, you can see that these users have access to all projects and these users only to some projects.
You can also create a new organization in here.