Contrast ratio is worked out by taking the darkest black and lightest white on a screen and comparing the luminosity.
EIZO says it's the 'magnitude of difference in perceivable brightness shown on a monitor's screen, from the darkest black to the lightest white,' which basically means contrast ratio tells you the difference between the two points.
For example, the ColorEdge CG276 has a contrast ratio of 1000:1 which means the brightest white point is 1000 times brighter than the darkest black the monitor can display.
A display with a high contrast is often desired, as this tends to mean you'll be able to distinguish between more shades, but it's not always necessarily better. If the contrast ratio is too high, for example, sometimes shadow colours can be too firm, making images appear stiff and this makes it difficult to match colours with output.
The ability to adjust contrast ratio can be used as a criterion for choosing a calibration monitor but do remember the effective contrast seen by someone using a particular display can be altered by the room they are working in so this is why it's important to set up the right environment. This includes minimising reflections from outdoor sources, using monitor hoods to block out indoor light which can cause reflections etc.
For more tips on creating an environment suitable for accessing prints, take a look at the EIZO ColorZone features section. You'll also find more monitor tips over in techniques.
For more details on the EIZO ColorEdge range of monitors, take a look at the EIZO UK website.