The Pulfrich Phenomenon was first described in 1922, by Carl Pulfrich, who described how a delay in processing the signals from one eye could result in targets moving in variance to reality. The Pulfrich effect is caused by a delay in conduction of the impulses from one eye to the brain. It can be induced by darkening one eye- by wearing a tinted lens in front of only one eye, but may also be induced by reducing the light using a pinhole. It may also occur after vascular accidents, episodes of Multiple Sclerosis causing Optic Nerve Inflammation (Optic Neuritis), and trauma to the nerve.
To see the 3D effect in these videos, all you need to do is look at the screen with both eyes, but hold a tinted lens in front of one eye, the videos advise which eye should be darker.
It can be a troublesome thing to live with- when not used as a demonstration- imagine perceiving everything going left to right coming closer and things going right to left further away, but it may be relieved by prescribing a tint to the unaffected/ undamaged side of the visual system to rebalance the speed of conduction.
Though I did not personally see this person, a lecturer at my university told a story about a man who had had an accident, and damaged one of his optic nerves, inducing the Pulfrich Effect. The first day he was released from the hospital he was shaken and had to get off the bus home, because to him, it seemed that every bus that passed the one he was on going in the other direction looked like they were going to smash into the side of “his” bus. The Pulfrich Effect can be induced by a reduction in brightness coming from one eye, and he was prescribed a pair of spectacles with a specific tint only for the undamaged side, which compensated for the damage and removed the effect.
People suffering difficulty because of the Pulfrich Phenomenon who have been prescribed with unequally tinted spectacles have reported improved abilities to drive, aim (even a cup of tea into the cup instead of the saucer!) and navigate stairs and unfamiliar places. Further information on the Pulfrich effect is available in this Wikipedia article, and in this article co-written by the University Lecturer mentioned.