how the windows polarize and unpolarized on the Boeing 787
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Exactly the same way an LCD screen works, but it helps if you think of the old LCD screens on digital watches and the like.
There is a crystal which, under a small electrical voltage, will change the structure of itself so that the polarity of light allowed through it alters.
In the old watch LCDs, this was then combined with another layer that polarises light in the other direction (horizontal/vertical). So when you look at the watch when it has no power, you’re seeing only horizontal-polarised light getting through. When you apply voltage to the parts of the crystal display, they polarise vertically. That means that – in combination with the other polarised glass, nothing gets through, so it appears black, and hence you can read the numbers on your watch.
If you take one of those watches apart, both parts actually look clear, but they’re just polarising the light in different ways and combine to form a black area when you apply a voltage to the liquid crystal part.
Windows that have the same effect have been sold for years, they are often used as privacy screens etc. in offices, that can become dark or see-through at the touch of a button, by applying a voltage to the liquid crystal inside. Or, in your example, polarising the light so the pilot can see.
Your LCD monitor and games consoles and tablets and smartwatches all work on the same principle, just much more finely. They show red, green and blue shone through the back all the time (the “backlight”) in each pixel and then by selectively covering up on or more of the colours for each pixel by a given amount they can display any colour combination you like.
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