Our eyes and brain do things on a daily basis that make LSD's effects seem relatively tame.

One of the things our brains do is a color balancing activity of their own. No one knows why for certain, but its theorized we do it so that it would be easier to track prey as they dodge in and out of shadows (prey reflect the blue sky while in the shadow, so they become bluer). Regardless of why, our brains do it.

This is remarkably obvious if you are a diver. Reds get cut out by the water column rather rapidly. In fact, at 30m, red is a camouflage color. However, we don't perceive this when we dive. We think we're seeing perfect colors. Hold up a white card in 30m of water, and it looks "white" to you.

Now take a picture of that card. The camera sees raw photon counts. It's going to call it like it is. Far fewer red photons will hit the camera, so it will record less red in the picture. No problem!

The need for color balancing comes when you try to view those photos when you aren't 30m under water. Your brain will do its color balancing thing, like it did underwater, but now it does it with respect to the perceived lighting in the room. If you're in a reasonably lit room, your brain will tune itself to perceive a white object (like the unprinted white rim around a photo) as "white." Now the picture looks horribly blue. This is an accurate model of how many red photons hit your eye when you were at depth, but now your brain is no longer color correcting for it.

The solution is white-balancing. You pick a "white" object in the picture (which is actually a bunch of blueish pixels), and declare "I want people to think this is white." The software does some color mapping to effectively do what your brain was doing before. Once printed, this region of pixels takes on the color of the light in the room (usually rather yellowish), but now your brain properly does its corrections, and you perceive white!

That's almost the end of the story. This works remarkably well for printing. On a screen, the brain has a little more trouble making good guesses at color corrections because the brightness of the screen does not scale with the light in the room around you. If you're editing a photo professionally, its common to pick a room with very constant lighting, and "color balance" the monitor so that things it shows as "white" show up as "white" when printed!