When setting up an Instructor Led Course (ILC), you have the option as an admin to require that an enrollment requires approval. You can find this option under the Availability tab when setting up you ILC.
If you have this option enabled, users will not be enrolled until an administrator (or other user depending on the option you choose) manually approves the enrollment. If you want the administrator to be notified that they are required to check on, and approve an enrollment, you will want to do so in the Messaging tab.
Please note: If this message is not enabled, your course editor, supervisor, administrator, or other user will not be notified of new session enrollment approval requests.