Datasets have two permission levels, public and private. Public datasets are accessible to all visitors of your domain and can be discovered through the site-wide data catalog. Private datasets can only be accessed by the dataset owner, users on the site with the appropriate permissions, or users with whom they've created a share with using the Sharing tool. You can read more about permissions here.
To change the permissions on your dataset, click on the "Manage" button to open the Edit sidebar, then click on "Permissions". Where it says "This dataset is currently public" or "This dataset is currently private", check the box next to your desired permission option in the box below. Click "Update" to save your changes and close the sidebar.
Note: It may take up to 15 minutes for your dataset to be re-indexed and for the site-wide data catalog to be updated. The actual permissions change, however, occurs immediately.