One poster said it best. It is Lego for Developers. The benifits of building sites like this cannot be measured. It might seem more complex at first, but once you start using it - you will never want to go back. Maintaining a site is far easier with this method, and the site will scale much better.
The difference between a "Framework Plugin" and a normal "PHP include" is that you don't need to remove head tags, body tags, etc... from the included file. All you do is create a full page the way you normally would - then the framework includes it properly into the master page. It puts the head within the Head - and the Body at the location it needs to be.
Where would you use it? Others may use it differently, but this is what I do.
1: I create a master page - usually this would be the index.php page.
2: I create several other pages and put them in an "include" folder. These would be "header.php", "footer.php", "menu.php", etc.... (create whatever you need)
3: Insert all these elements where you want them on your main page.
If you were to create a static site from here - you would simply copy the index.php page as needed to create "contact", "about", etc... etc.... What happens when you want to change the footer? In the past you would have to update every file on the site. Well - now it is easy. Edit the footer file - and all the files automatically display the change. Same for the header and menu.
I create dynamic sites, so I don't re-create layout files. My content area is done with "dynamic plug-ins". I load the content based on a URL variable. All the sites content pages would exist in a folder such as "includes/content" and the content area will load each page based on a URL variable (?page=contactus). Of course - better yet you can get into Friendly urls but that is a completely different subject.
Essentially the main page in the site becomes more of a controller - and by separating all the elements of the site (header, footer, menu systems, ad boxes, etc...) it makes it much easier to maintain them going forward.
One final note: The includes files does not have to be static :) It can be recordsets, photo galleries, shopping carts and yes - it can even load it's own plugins - both static or dynamic. It's very - very powerful.