The square box in the camera view represents the renderable area as defined by the render resolution. The red dotted-lined-box (created with SHIFT + B) defines a 'renderable region' which allows you to focus on specific areas of your render - It's a great feature for fine-tuning.
Thanks. I also discovered the 0 key which appears to show the output from the point of view of the camera, and as far as I can see the red box seems to only work after pressing that. It seems that when I have pressed the 0 key I can zoom in but as soon as I turn the model it zooms out again. Is any of this covered in any of the lessons? I have been going through them in order and haven't come across it yet.