An organization is tied to a subscription, thus there is one organization per subscription. A subscription is effectively the way you pay for the services you use in your organization, through credits. The administrator manages the people allowed into the organization (members) and thus, the people who consume credits the organization has. The administrator has full control over the organization and all members, groups and items inside the organization. The administrator can monitor credit consumption. The administrator can configure aspects of the organization, for example, if members of the organization can see items that are outside the organization (part of ArcGIS Online as a whole), if members can share content outside of the organization, what area of the world the map should show by default, the gallery of maps and apps, and so on.Groups are collections of people that share a common interest. They may be working on a project together where they need to share maps and data with each other. Anyone in the organization can create a group and invite others (in their organization or other organizations) into their group. Members of a group can share items, but the member retains ownership of the item (others can't modify it). The group owner can remove members and content, if necessary.Hope this helps,Mike