How are line pairs and pixels related in image resolution?
The spatial resolving capability of an optical system refers to its ability to distingusih between closest (and possibly tiniest) details. The distance between a pair of lines, yields a measure of how small the distance between them can be while they are still sperated from each other. Resolution depends on several factors such as brightness level, color, and environment.

Those resolution (line) charts are designed to test optical equipment and systems, including your eyes too. Consider two black lines (with some thickness) viewd at some length and let them come closer under your control. It's known that at some small distance, you can no longer tell that there are two lines, but they will seems like a single one. That distance is the limit of your optical resolution. To get rid of the viewing distance dependence, the resolution can often be stated in a spatial angle unit.

That's also true for a camera system. It's spatial resolution is limited by two factors; first the resolution limit of the lens (its sharpness), and then the resolution limit of the CMOS / CCD sensor grid (its sampling density).