The above is true. Minor clarification though: the "dpi" (dots per inch) rating on a printer will measure the density of dots produced by the printer per inch of printing surface (this is also called "spatial resolution," an image's printed resolution). A lot of people also confuse input resolution with output resolution when working with printers. For example, take a printer that is rated to print up to 4800x1200 dpi (typical for today's market). Now let's say that you have a digital image that is 4800x1200 pixels. These two resolution ratings are VERY different. The image file actually populates 5,760,000 pixels on your display. The printer's rating is how many DOTS the printer is capable of printing PER inch of surface (i.e. your paper). Depending on your print settings, a printer can lay down multiple dots to form just one pixel from the original image file. And generally, the more dots it lays down for one pixel, the more definition your printed image will have because there will be less "gaps" between printed dots. This is the reason why a image file that represents only 300 dpi of density (again, this file might be say, 2400x1200 PIXELS in size, but will be sampled as 300 dpi) will still produce a terrific printed photograph in most cases. Printing in your printer's maximum resolution will just lay down more dots where there normally be only perhaps one or two in a lower resolution. This especially helps when you print out 8x10 and larger photos. This is also why 72 dpi looks great on an NTSC television. Given the pixel count of the television which is quite low in comparison to a computer monitor, 72 dpi is the sweet spot.
So in essence, when you actually shop for a printer, keep in mind that the manufacturers will overemphasize resolution on their printers as a true measure of image quality. Sure, more resolution definitely helps, but there are other factors that contribute to overall print quality as well. For example, the size of the droplets (measure in picoliters) that printer lays down will effect your quality, as well as the broadness of the printer's color gamut in its ink set.