“Resolution” is a word that is used with little concern for its multiple meanings, in computer equipment marketing. The word suggests a measure of what an observer (perhaps the human eye) can resolve; yet we regularly see advertisements for printers whose resolution is 1200dpi — far finer than the unaided human eye can distinguish. The advertisements are talking about the precision with which the printer can place spots on the printed image, which affects the fineness of the representation of fonts, and the accuracy of the placement of glyphs and other marks on the page.
In fact, there are two sorts of “resolution” on the printed page that we need to consider for (La)TeX’s purposes:
In the case where output is being sent to an intermediate distribution format, that has potential for printing (or displaying) we know not where, the final translator, that connects to directly to the printer or display, has the knowledge of the device’s properties: the DVI processor need not know, and should not presume to guess.
Both PostScript and PDF output are in this category. While PostScript is used less frequently for document distribution nowadays, it is regularly used as the source for distillation into PDF; and PDF is the workhorse of an enormous explosion of document distribution.
Therefore, we need DVI processors that will produce “resolution independent” PostScript or PDF output; of course, the independence needs to extend to both forms of independence outlined above.
Resolution-independence of fonts was for a long time forced upon the world by the feebleness of Adobe’s Acrobat Reader at dealing with bitmap files: a sequence of answers starting with one aiming at the quality of PDF from PostScript addresses the problems that arise.
Resolution-independence of positioning is more troublesome: dvips is somewhat notorious for insisting on positioning to the accuracy of the declared resolution of the printer. One commonly-used approach is to declare a resolution of 8000 (“better than any device”), and this is reasonably successful though it does have its problems.