Is it something that happens in the real world?
No, but many people think it does because they are translating "my eye appear to be a different color" to "my eyes are a different color". Those things may seem alike, but they're different. The basics of how it happens that when we're in this or that mood we hold our head in different ways and it can effect things like how blood shot our eyes are or the direction of light/shadow hitting our eyes. The result is that that Eyes can appear to change color, because of the colors around them.
Is it something that could be possible?
Yes indeedy it can be done. How? Basically the same way pupils can dilate. Just have a similar thing that comes over the pupil (in the standard 3 colors) that developed to be able to modify what light goes in the eye so that some things will stand out more or less because certain wave patterns will be blocked out. It would be a rather useful trait for a predator on Earth... but I don't know how the prey would evolve to counter it.
You could say that it is controllable in wild animals, but in the humanoid animals you could say that they lost the ability to actively control it resulting in the various lenses closing/opening when they are focused, in a rage, etc.