This is an interesting phenomenon which I have been aware of for several years, but I haven't yet come across any official description of it or explanation for it.
Nonetheless, the phenomenon is easy to explain. It is a result of light adaptation in your retina responding to different levels of light being received by each eye.
The level of ambient light present over the course of the day varies by as much as 10 orders of magnitude, and our visual systems have evolved to account for this. The human retina and later visual processing centers have a number of ways to adapt to the light level present in the environment. They are constantly doing this, but these adaptation mechanisms take a little bit of time to adjust to a different light level, usually on the order of fifteen seconds to a few minutes. This is why when you step out of a dark room into the sunshine, you are momentarily blinded by the (relatively) bright light.
Some of these adaptation mechanisms are color-specific, such as those that occur in the cone cells themselves.
TL;DR-ers, just read this section
Most of the time, both of your eyes experience roughly the same levels of light intensity, both in general and for each color of light. But this is not always the case.
If you have one eye covered for a period of time, such as when you've been laying down, then your two eyes will be adapted to two different sources of light. If you then uncover that eye, then for a short period of time that eye will perceive the world to be brighter than the other eye. If the light level present in the environment has a tint to it as well, then the just-uncovered eye will perceive that tint more strongly than the other eye.
DIY Science Time
You can verify this yourself, like I have been doing over the past hour, with nothing more than a makeshift eyepatch and nothing better to do.
- First, check your initial state by closing one eye and then the other and switching back and forth rapidly while looking at something white. If you've been awake and active, the images from each eye should appear to have roughly the same hue and intensity.
- Cover one eye completely (without pressing on it) for a period of about five minutes, while leaving the other eye open.
- Then, remove the eyepatch and alternate closing each of your eyes again.
If my hypothesis and explanation is correct, the previously-covered eye should see the world as slightly brighter and more strongly tinted than the uncovered eye does (the hue of this tint should depend on your light source).
If you guys actually do this, you should report your results in the comments, especially if your results demonstrate a flaw with my hypothesis. Let's do some science, people.