I fail to understand how the definition of "Private Cloud" matches with the definition of cloud.
I think you might find this article helpful in trying to see how it all fits into Cloud Model.
A cloud is just a data center that has data that can be accessed anywhere, you having a data center that can only be accessed internally; by your company is a "Private" cloud.
Welcome to the course. That is a great question! Private cloud is used solely "on-premises" by your organization. This is where you bring cloud services internally. For example, using Amazon S3 on Outposts.