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Resolution values mean different things at different points in the post processing, uh, process.
When the image arrives in your image processing application (such as photoshop) the program essentially assigns a resolution, often the 72 figure that you see. But at this stage, the value is largely irrelevant.
When you print, the story is different. At that point you'll specify two things. One is the height/width dimensions of the print, corresponding to how large of a print area you want to fill on your paper. The second is, again, "resolution." Here, resolution matters. You are unlikely to be happy with resolution much lower than about 200, and many consider 180 to be an approximate lower limit for high quality large prints. There are a number of thoughts about the best resolution values to select when you print, but rather than "go there," let's just say that something in the 200-300 range is probably usually fine.
At this stage, if you select a specific image size (height x width), the number of pixels in the image may not quite match up at the resolution you select. Here the image size dialog box lets you make these specifications and then "interpolates" (essentially, invents additional pixels as needed) to produce the pixels you need for the print.