I thought I understood - but I don't think I do.
Say you have a line 1 inch long that is 1/72 of an inch thick. On Mac OS X (and Mac OS before it) that one inch line would be defined as 72 points long and one point thick since Mac OS X defines it point space (what you draw in) as having 72 points per inch.
Currently Mac OS X defines that one point maps to one pixel on a display.
So if you had a display that had 72 pixels per inch (physical pixels crammed into one inch of length along the display's surface) then a 72 point long line would appear to be 1 inch long on that display. Now if you had a display with 144 pixels per inch then a 72 point long line would appear to be 1/2 inch long on that display and on a 288 pixel per inch display it would appear to be 1/4 inch long.
So as you get displays that can cram more and more pixels per inch your on screen drawing will appear to be physically smaller and smaller unless you adjust the scale of what you are drawing. In other words as the fidelity of displays approaches that of common laser printers you need to adjust what you draw to use more pixels so it maintains the same appearance in terms of physical dimensions.
This is what
resolution independent UI is about... Mac OS X in the near future will allow you to (or possibly automatically) set the scale factor for the visual environment to match the physical size of pixels of your display.
For example if you had a 144 pixel per inch display you would ideally set the scaling factor to 2x. That would mean a 72 point long line (aka 1 inch long line) that is 1 point tall would be displayed on your screen using a rectangle that is 144 pixels long (72 x 2) and 2 pixels tall (1 x 2). In other words that 1 inch long line would appear as 1 inch long on your display instead of just a half inch long and it would be displayed using twice as many pixels... which means you have a higher fidelity image.
It should be noted that since day one Mac OS X has utilized a resolution independent drawing environment (Quartz / Quartz2D) and that is how what you see on screen is appropriately scaled when you print it out on say a 600+ DPI printer without out much of a through by a programmer (at least for those using modern APIs based on Quartz or using Quartz directly). What Apple is currently doing is starting to utilizing this existing capability to scale what is drawn to the screen since screens are improving in DPI.