I was looking at my digital watch on the way to work, and I couldn’t read it because the screen was black. I tilted it around, and noticed that it was black only at a 45 degree angle. If I tilted it to -45 degrees, it was fairly bright. Now that I am at work, the display is readable at any angle. In the truck my watch was in bright sunlight and I was wearing sunglasses, which I didn’t know were polarized but I suppose must be to cause this effect. So what do you think, ye science-minded?
Yep. LCDs have a polarizer in front of them. When energized, the LCD segment polarizes the light passing through it, and only becomes visible when seen through a properly-oriented polarizer.
Yep. You can get (kinda) the same effect some days when the sunlight is polarized. (It’s low on the horizon? Most of the light hitting you is incidental? I forget. It happened to me once).
IIRC, the polarizer on most calculators is at a 45 degree angle. This means if you take your calculator apart and flip the polarizer over, the display is inverted (the background is black and your numbers are white). That is, if you’re the type to take calculators apart. 
I did some searching around and found this site on LCD screens, pretty interesting stuff.