Advanced Permissions is not enabled by default. To enable it, navigate to Dashboard > System & Settings > Permissions & Access > Advanced Permissions. Click Enable Advanced Permissions in the page that appears.
Things to keep in mind
Advanced Permissions is Permanent
Once Advanced Permissions have been enabled on a site, you cannot revert to Simple Permissions. Advanced Permissions introduces changes to your site's database that cannot be undone. If you're not sure if Advanced Permissions are necessary for your site, we suggest you back up your database before enabling this set of features.
The admin Superuser
Regardless of how permissions are set, the "admin" superuser will always have access to deleting, moving, changing permissions, and otherwise editing pages. If you manage to break something, you should be able to restore access by logging in as admin and changing your settings back.
Note that admin is the default account that was created when you set up your Concrete CMS site. It's a special user, not simply a user in your Administrators group.