This is one of my favorite optical illusions and it's neat to see it demonstrated on video. I like it because it reveals how facial recognition is a discreet neurological process (or processes as The Neurophilosopher has reminded me).
This illusion may be caused by specific psychological processes involved in face perception which are tuned to upright faces. Faces seem unique despite the fact that they are very similar. Humans may have developed specific processes to differentiate between faces that rely as much on the configuration (the structural relationship between individual features on the face) as the details of individual face features, like the eyes, nose and mouth. When a face is upside down, the configural processing cannot take place, so minor differences are more difficult to detect.
Interestingly, this effect is not present in people who have some forms of prosopagnosia, a disorder where face processing is impaired, usually acquired after brain injury or illness. This suggests that their specific brain injury may damage the process that analyses facial structures.