The resolution of a printer or a scanner is measured in dots per inch, abbreviated "dpi." If a printer has a resolution of, say, 300 dots per inch, that means in one inch there are 300 dots in a row across, and 300 dots in a row down. The more dots per inch, the smaller the dot has to be, of course. You can logically understand, then, that the higher the dpi, the smoother the printed image will appear to be.
You may hear the resolution of a Macintosh screen, or monitor, measured in pixels per inch, or "ppi."