Hi Robert,
The main reason for using django rest framework is if you need a backend to communicate with one or more rich frontends. An example could be if you have a website running django and you want to create a mobile application for iOS or android. You can then create an API that will communicate with your django server via the django rest framework.
There is also a vast difference between the django admin site and the django rest framework. I normally use the Django Admin site to add items to the database that are needed for my datamodel. For example user groups with permissions. The django rest framework creates a complete REST API with json or xml representations of your models. However you can also browse the API via HTML to check what it looks like and also use that as the documentation of your API. That can also be switched (I think).
Django Admin cannot be used as a REST API for you models, but you are able to add / search and delete your data.
Hope that helped a litte!