A calibrated monitor will display photographs accurately and as intended by the photographer. When calibrated a monitor accurately displays black, white and all shades and colors between (at a specific gamma and color temperature but lets not get too technical).
Calibrating a monitor can be simple but is actually a very complicated subject. Possibly your monitor came with software to adjust it; use it. The best solution is a hardware calibrator like the Spyder or eye-One.
If you don't have any of those programs you can start with the following simple procedure. The first thing, and one of the most important, is to get the black point set. Examine the black area below:
The large black area should be as dark as you can get it. In the center of the black area is a 5% lighter square. This square should be visible. If it is not visible your monitor is too dark. If the inner square is bright you're monitor's brightness level is too high. Either way you need to adjust the brightness level. Start with your contrast and brightness turned up to maximum and slowly adjust the brightness down until the center square disapperas. Now increase the brightness until the square is just visible.
You should now be able to see all steps in the gray scale below while keeping black nice and dark.
No color should show in any of the shaded squares above. If any trace of color is visible you need to adjust your RGB balance. That procedure is more involved and beyond the scope of this article so google it for help. Several websites have good procedures online such as The Lagom website.
Portions of this webpage's code from the original Pleades-Astro monitor calibration basics page; used with permission.