What is a page?

Maybe I'm missing a previous post, or something in the user documentation, but what is a page? On a select few groups there is a New Page option in the +New button, which creates a /p/ URL (as opposed to the /f/ for forum, /w/ for wiki). I can't figure out how this is enabled or how it is even an option to add to other groups. 

Looking at the groups that do have it enabled I think there are some great possibilities to create layouts, but I'm baffled as to how they even come to be, or even the option to create one. 

Appreciate clarity as to what this is, how it's used, and how to enable it.