This mode is quite useful when using a legacy manual focus lens on an adapter. To demonstrate how this mode works on the Sony NEX-3N, I mounted an old Nikkor 24mm f/2 AIS lens to the camera, using a Nikon AI to Sony NEX adapter. Using the lens on a 1.5x crop camera, it becomes like a 36mm lens in terms of field of view.
I placed some lenses on a table, to demonstrate how the focus peaking highlights the borders when a part of the image is in focus. I set the lens to f/2, f/5.6 and then f/11. At f/2, only a thin part of the image is in focus. At f/11, you can see that much more is in focus. The camera can be set to display the peaking highlights in white, red and yellow. I selected yellow in this demonstration.
This feature works the best when there are strong contrasts in the subject. With soft, organic shapes, it tends to not work as well, as there are fewer edges to be highlighted by the algorithm.
The focus peaking feature works when using legacy manual focus lenses, but also when using native Sony NEX E-mount lenses. What's more, it also works fine during video recording, which is very useful. I get the feeling that the algorithm is somewhat optimistic, meaning that it can categorize areas as being in focus, even if they are not in perfect focus. Then again, for critical inspection, you can still easily bring up the magnified view by clicking the upper control button.
Within the Micro Four Thirds system, the focus peaking feature is sadly not as commonly implemented. The most recent Panasonic model, the G6 has the feature, and so does the Olympus PEN E-P5, but no other models, at this time.
When the premium Panasonic GH3 was released in December 2012, a Panasonic engineer was quoted saying that no future firmware upgrade could add the focus peaking feature to it. However, a later interview stated that this might be possible, after all.
On one hand, it does not make sense for Panasonic to continue enhancing an older model: Spending the effort on new models make much more sense. On the other hand, if they make the GH3 even more attractive, they can sell a bigger volume of them. It does have at least one more year as a premium camera in the Panasonic lineup.