those files will be opened with google docs web app. the web app itself can work offline. so your docs work offline.

How do I enable this feature? Whenever I try to access my docs offline the page simply does not load.

I am using a google apps account if that makes a difference.

There is an option in settings drop down from top left of the homepage od docs. Also the offline url is https://docs.google.com/offline. But you need to set up offline first from the menu i wrote about above.