They're LCD screens without the reflective part. There is a polarization filter and the liquid crystal. When the polarizations are aligned it lets light through. You can control the polarization of the liquid crystal by applying a voltage. The greater the polarization mismatch the more of the light that is filtered and the darker the window.

It's the same idea to taking two polarizing filters and rotating them relative to each other. Instead of mechanically rotating one filter you adjust the molecules with an application of electricity to change the polarity.