I read through the article and it does a nice job of simplifying the science behind polarization. A HUD takes advantage of the partial reflection of light by the windshield. Some of the light from the screen mounted in the dashboard is reflected off the windshield and back at the driver. The screen mounted in the dashboard is an LCD screen which emits polarized light. So, the light reflected back at the driver is also polarized (meaning that it is all oriented in the same direction.) Polarized sunglasses have thousands of tiny lines which are oriented vertically. If the light emitted by the LCD screen is not polarized with the same vertical orientation, then it will not pass through.
The simplest analogy is to think about looking through two picket fences. If you have two fences which are both oriented vertically (0 degrees from each other), then you can see through them. But, if one fence is oriented vertically and the other is oriented horizontally (90 degrees from each other), then you wouldn't be able to see anything. Any orientation between zero and 90 will reduce the amount of light, but still allow some to pass through. If you try rotating your head when you are wearing polarized glasses, you will see this effect because the HUD will get brighter/darker depending on the orientation of your glasses compared to the HUD.
Hope that helps a bit!
