Private repositories on Cloudsmith allow users to store and manage their own Terraform modules securely. Uploading a module involves creating a new module in the Cloudsmith interface, adding required files and metadata, and then uploading it to the repository. Downloading a module is done by navigating to the desired module's page, clicking "Download", and selecting the Terraform version to download for. With private repositories, users can control access to their modules, ensuring only authorized individuals can view or modify them.