When we mix 100% green with 100% blue we get cyan. A transparent sheet of cyan film therefore allows green and blue light, yet absorbs red light. If we take a digital photograph (composed of red, green and blue light) and view it through a transparent cyan film, the film absorbs the red light allowing only green and blue to pass. In theory, if I have two photographs and I remove all the red from one, then I view both through transparent cyan film, I won't be able to tell the images apart. One's image emits no red light; the other's red light is blocked by the "filter" - in neither case does any red light reach the viewer.
What if we view an image with only red through our cyan filter? There is no green and no blue light in the image, and all red light gets absorbed by the filter. The image will appear black.
IMAGE (red only) (green/blue only)
FILTER (red) (cyan)
EYE (left only) (right only)
Now, put on an imaginary pair of red/cyan glasses and look at two digital photographs side by side. Close your left eye (red filter) and look with your right eye (cyan filter). Remember, an image with no green or blue appears black through cyan, so we remove these colors from the left image. An image with only green and blue appears in green and blue (there's no point in having red in the image as it would be absorbed by the filter anyway - plus it would destroy what comes next). With only your right eye, the left image is black and right image is visible. Now, close your right eye (cyan filter) and look with your left eye. The right image has gone black because it doesn't have any red - the green and blue have been absorbed by the red filter. The left image springs to life now, because it has red in it. We have found a way to show each eye a different image - and our brains do the rest.