The diffuse mode could be thought of as a flashlight set so that it casts its light very broadly, but not very strongly in any area. (As opposed to the Focused mode, which would have its light cast very strongly in a single area but very weakly everywhere else.
You are in focused mode when you are deliberately thinking about something. This might be when you are focused on solving a familiar type of problem, driving on a busy road - i.e. doing something that requires your concentration.
You are in diffuse mode when your mind is wandering freely. Some examples of situations when you are probably in this mode of thinking are when you're drifting off to sleep, taking a shower, brushing your teeth, relaxing with quiet music, or going for a walk.
Switching from focused to diffuse mode can be as simple as walking away from your desk to get a drink - the thing to remember is that diffuse mode involves your thoughts meandering freely. You can't force yourself to start thinking in diffuse mode about a particular issue (consciously directing your thoughts like that means you are in focused mode), but you can influence it. For example, reading over notes or a to-do list before going to sleep is likely to direct your subconscious thought towards what you've just read. Likewise, leaving a problem you're working on to go for a quick walk may encourage your diffuse mode thinking to turn to that problem.
During the course of the past couple of years I was writing software that performs certain algorithmic and sometimes pretty complex mathematical actions. Several times I did find myself struggling to get the high-level math concept working correctly in the details in the program code. I kept myself focused for several days in a row often forgetting to eat, unable to sleep and having all other nice signs of obsession. All of these times I did find the right solution only after relaxing. Actually it came by itself in it's completeness, when I went for groceries or finally fell in deep sleep. Then, the very last case like this I was sitting with my laptop three days in a row somewhere in a village, near trees where birds were singing, I was drinking tea, breathing fresh air, and switching between being focused and diffused several times a day. The puzzle was way more complex, but I did solve it with less bugs and, what's more important, with minimum stress.