I believe resolution indepence means an icon (for example the Apple menubar) will look the same size (and quality) regardless of the resolution of the display (hence the term resolution indepence), that is the space an item takes won't be defined by pixels (which have varying physical properties) but rather actual physical measurements, for example an item could defined as occupying an inch instead of 50 pixels for example, so the item will look 2 inches at any resolution as opposed to extremely big in low pixel density resolutions and extremely small in high pixel density resolutions.
I could be wrong though.