What to see
Observe the face on the right: do the eyes have the same colour?
If you're like me, the left eye has a blueish tint, while the one on the right a neutral gray. And, as you probably guessed, both eyes actually are without colour and thus identical.
[Yes, it's a famous person, though manipulated: I merged two right face halves, one flipped, so the eyes are really fully identical.]
What to do
You might well argue that I manipulated the colours on the left, obviously there is this large red translucent overlay. With the slider you can change transparency: The two eyes look identical, when the overlay is fully transparent; when the slider is fully up you can observe the hole I cut, so the overlay does not cover the iris. So the eye colour is not physically affected by the red overlay.
You can try this with different colours using the colour picker above the slider. For me, the effect is strongest for a red mask.
There's more you can try: first, place the mouse pointer over the "Mask" checkbox, don't click yet. Then fixate the nose right between the eyes steadily for 10–20 s; click aftwards, not changing your gaze: The eye turns red, for a little while at least!
This is a case of simultaneous colour contrast, and probably also of colour adaptation. The redish tint next to the eye shifts the neutral gray of the eye to the opponent colour, which for red is blue-green. Also, when your gaze travels around the red part of the face, the central part of your retina adapts a little to red, so when it is presented with a neutral gray again, the opponent colour is seen (same mechanism as in the Lilac Chaser). You can disentangle these two mechanisms: turn off the mask, let your eyes return to neutral adaptation, fixate the left eye and turn on the mask: For me, a blueish tint is immediately present (simultaneous colour contrast), but increases over seconds (additional adaptation). Yet these explanations don't fully cut it for me: the effect already occurs at quite high transparency (30% opacity, as preset) and gets weaker when you push the slider very high. I'll have to dig into the literature…
I found this idea here.