It's actually really simple. The display works in a way that you control the polarization of outgoing light (but the intensity is constant). Then you filter whichever polarization you want. So a black dot on a white screen could be achieved with a small vertical polarization region on a horizontal pol. background, and filter out the vertical pol., with a polarizer horizontally aligned. Align it vertically, and you swap the intensities.

Note: In this case the light whose polarization is controlled is the reflected incoming ambient light, which isn't polarized; in a computer monitor it's the back light.