Sometimes this is given as two numbers such as 1440x720 dpi or as one number, such as 600 dpi. The 600 dpi number usually means it is 600x600 dpi and the other dpi listing is giving two numbers because it is different by for the horizontal and the vertical dpi. Many electronics stores like Best Buy have printers out where you can print samples, and I suggest you do this to see which looks best on the types of printouts most important to you. Also consider the type of printer. Inkjets are inexpensive but provide color printing.
Most lasers are greyscale only, but are high print quality.
Color lasers are very expensive, but usually have good quality. The less common wax-based printers provide great color image quality, but are also expensive.