Basically, how it works is you can divide each pixel three ways horizontally: R, G and B, because a full color square pixel is actually three vertical, rectangular, monochromatic bars.
So, what you do is you have a background color, say {1, 2, 3} and a foreground color {100, 101, 102}. Your pixels may be aligned something like this, for a three pixel horizontal line:
{1, 2, 3} {100, 101, 102} {100, 101, 102} {100, 101, 102} {1, 2, 3}
You can make this line look like it's one third of a pixel longer by changing the color of the last pixel:
{1, 2, 3} {100, 101, 102} {100, 101, 102} {100, 101, 102} {100, 2, 3}
...Or, the first pixel:
{1, 2, 102} {100, 101, 102} {100, 101, 102} {100, 101, 102} {1, 2, 3}
Basically all modern full color monitors have the same R, G, B pixels (it is the standard), but it is true that this technique won't look right on a rotated monitor. Also, it only increases the horizontal resolution.
It is a technique that is used mostly for font rendering, since fonts (Latin fonts especially) really benefit from the extra horizontal resolution. Though, it can definitely be used in pixel art as well.
Here's an example of a tilted line done using subpixel anti-aliasing, at a normal resolution, then at 8x zoom.