You have a source of light (for simplicity, we'll say it's a backlight), a polarizing filter, the "liquid crystal" itself, and another polarizing filter. The liquid crystal changes the polarization of the light that passes through it, in an amount that changes when you put a voltage across it. So in one condition the light is able to pass through both filters and you see white or color, while in another it ends up cross-polarized and you see black. The description is a bit fuzzy because I'm too lazy to look up whether the filters are aligned with or against each other, and whether voltage makes the crystals rotate the polarization more or less... but that's the idea of it.
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