When displaying letters in small sizes, the pixel grid becomes increasingly coarse and the result often becomes ugly and less readable. To prevent this, "hinting" instructions need to be built into the fonts to help the type rendering, by fitting the horizontal and vertical strokes to the pixel grid, aligning heights, and so forth.
System fonts provided with Windows are professionally hinted, as are many professional webfonts. On the type rendering environments on Windows, hinting makes a huge difference.
The problem is, TrueType hinting—indispensable for TrueType fonts on Windows—is a complex, tedious process that only a very few specialists are able to do. I heard a few years ago that there was only one person who had the expertise to perform TrueType hinting on hangul (Korean alphabet) fonts.
The result is that many if not most fonts are either unhinted or more or less automatically hinted (which is recognizably below the quality of manually hinted fonts) as many typeface designers find the prospect of TrueType hinting daunting. Manually hinted fonts are more expensive.
If screen resolution improved so that unhinted fonts would still look good enough, that would vastly increase the choice of fonts that we can use for the screen. It would also free typeface designers of having to devote a significant chunk of font development on hinting.
These types of issues are even more important for some other writing systems. Chinese characters, for example, can be very dense with dozens of strokes packed into a single glyph, and would be illegible at a modest size on the screen if the resolution was not high enough.
Apple's approach to type rendering is less dependent on hinting, and it is not a coincidence that Apple has been leading the pack on high resolution displays as a way around the problems of rasterization.
Further reading: http://www.rastertragedy.com/