The picture above shows a normal beach scene.
To see the colour illusion, you need to run the video. This is a Windows Media file, 1.7MB in size.
If we look at an image for a certain period of time, say 30 seconds, then when we turn away, we see an 'afterimage'. However the after image is the opposite colour of the original image. So if we stare at a black square long enough, then when we look away, we seem to see a white square.
This also works for colours, and this illusion uses this phenomenon. Initially we are looking at a negative image of the beach scene. The image then mixes into a black and white version of the same image. However our brain is at the same time showing us an afterimage of the original colour negative. The afterimage therefore now has the colours shown correctly. And so when we see what appears to be a colour picture of the beach, we are in fact seeing a combination of two images - the real black and white image, and the colour afterimage. The result seems to be a normal colour picture, until we move our eyes, whereupon the two images no longer align, and we suddenly see that in reality we are just looking at a black and white image.
We are very sensitive to detail in a black and white image - we see edges very clearly. However the colour information can be a lot less precise, and is still convincing. This is a basis of colour television - a sharp black and white image, with a layer of colour information added that is actually of a much lower resolution than the underlying black and white image.