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What is contrast in a projector

In a projector, the contrast ratio is the difference in brightness between the brightest white and the darkest black that the projector can display. Edit

How is this measured?

Each projector has a stated contrast ratio.
The brightness of the darkest black projected by the projector is measured and the brightness of the brightest white is also measured. The contrast ratio specifies how much brighter the white is compared to the black. For example a projector that projects whites that are 1000 times brighter than the blacks would have a 1000:1 contrast ratio.
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Does contrast matter?

Contrast only matters in rooms with effective blackout curtaining. In typical classroom environments the difference between a projector with a 500:1 contrast ratio and a 2,000:1 contrast ratio is difficult to detect.
In a room with heavy curtains the difference between a projector with a 2000:1 contrast ratio and a 20:000:1 contrast ratio is also difficult to appreciate.
The benefits of very high contrast projectors - 10,000:1 or greater is appreciable in rooms that are completely darkened.
In a room with effective blackout curtaining, dark colours and blacks would appear pale and washed out on a projector with a 500:1 contrast ratio.

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Different types of contrast ratios

There are two main types of contrast ratios, static and dynamic.

Static contrast ratio

The static contrast ratio is the measure of the contrast between black and white when both black and white content is projected in the same image. A projector with a high static contrast ratio can generally display detailed light tones and dark tones in the same image.
A high static contrast ratio would be 2000:1, an average static contrast ratio would be 500:1.

Dynamic contrast ratio

A projector with an average static contrast ratio can considerably improve the apparent contrast of the images it projects by using dynamic contrast - this is generally available on projectors designed for video and movies.
The projector adjusts the overall brightness of the image automatically to make dark scenes deeper and bright scenes brighter.
Specified dynamic contrast ratios can be very high - up to 20,000:1.

Static contrast vs dynamic contrast?

A projector with a 2000:1 static contrast ratio would provide superior overall contrast to a projector with a 2000:1 dynamic contrast ratio, especially for still images.
However a projector with a high 10,000:1 dynamic contrast ratio would generally be superior to a projector with a lower 2000:1 static contrast ratio, in particular when displaying video and movies to accomodate for bright and dark scenes.