Suppose you are part of an organization on data.world (see Creating an organization for more info) and would like to create a new project or dataset. You can choose to create the asset in your own account or within the organization's account.
In both cases, you will maintain control over the dataset or project. You can invite contributors, change visibility from private to public, and edit it to your heart's content.
When you create a dataset or project with the organization as the owner, you can choose whether to share it with the entire public, just the organization, or with no one at all. When you choose to share it with the organization as in the following image, the organizations members will receive View only permission by default (read more about permissions at Understanding permissions).
To change the permission levels later, go to the People tab from the project overview page or the Contributors tab from a dataset overview page. Find the organization and click on the dropdown menu under Access to modify the permissions.
If you had chosen to make the project completely private when you had created it within the organization, then you will need to go to that same People or Contributors tab to share it later. In that case, you'll see that the organization has a convenient Invite all members button next to their name. The organization will be added automatically - there is no need for an admin to accept the invitation. Again, those members will be given View access by default, but you can change that the same way as the last example.
Individuals can share a dataset with an organization exactly the same way they share with other individuals. Just go to the Contributors tab on a dataset or People tab on a project, and use the Invite button to add the organization.
Once added, the organization's administrators will receive a notification they can accept or reject. If they accept the invitation, the dataset will then be shared across the organization's top-level members using the same permissions the organization received.