This illusion works because the faces are of similar size and placement so your eyes initially interpret this as a stereo vision exercise. When the two images don't match, the parts of the faces that are different seem exaggerated because they stick out. Our eyes, and our brains, are well trained to notice discrepancies, or differences.
As Christians we live in a double vision world. There is evil and there is God. There is God's will and there is sin. There is the way we see things and the way God sees them. We try to make sense of it, and fail. The world distorts the values given to us by God. Some seem silly, others grotesque. Often what is cherished by the world begins to look normal to us. We see, but, we do not perceive. We do not interpret sin for what it is. The more sin distorts our view, the more distorted we become. This is not an illusion; it is reality.
The blood of Jesus covers our distortion as well as the multitude of sins that cause it. Because of the saving work of Jesus, when God looks at us He sees perfection. Jesus unites our image with His so we once again find ourselves in God's image.
In watching this video clip, when you keep your eyes on the cross the images are merged. When you take your eyes off of the cross you can only see one image or the other. In our lives the cross must always be uppermost in our minds. When we look at the cross we see Jesus translating God's love for us and transmitting it to us. When we allow our eyes to stray from the cross, we can see only the world. This view can only serve to dull our senses and distort our thinking.
You will indeed hear but never understand, and you will indeed see but never perceive." For this people's heart has grown dull, and with their ears they can barely hear, and their eyes they have closed, lest they should see with their eyes and hear with their ears and understand with their heart and turn, and I would heal them. Isaiah 6:9-10 ESV