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Mark has pretty much got it right.
Binning increases sensitivity and "effective pixel size" by effectively combining pixels on the chip, like Mark said. 2x2 means 4 pixels are joined as 1, 3x3 means 9 pixels are joined as one, etc.
Take 2x2: The advantages for astronomy are:
1) the light captured by 4 pixels is combined to 1, so you get 4 times the sensitivity/data in each resulting pixel.
2) the effective pixel size of the chip is increased, so instead of a pixel being 7u x 7u it would be 14u x 14u.
3) the download image size is smaller, so frame rate can be faster. a 2x2 image is litterally smaller in terms of the number of pixels digitised and hence downloaded.
Mark is right that you can use binning to achieve images with fainter nebulosity but really you could have achieved the same at 1x1, but just at a longer exposure time.
Examples of when binning are used in astronomy:
1) for focusing - increased sensitivity means shorter focus exposures are needed and smaller file size means quicker turn-around between focus images. Paritcularly useful on older Parallel Port cameras.
2) for colour - using RGB filters you get less data than a clear filter so longer exposure times would be preferred, binning colour at 2x2 while keeping luminance at 1x1 means you have stronger colour signal to improve colour contrast. Also, the colour channels don't need the high resolution data of the luminance channel (it would be better if all was 1x1 but in reality it makes little difference).
Google for "ccd binning" and you'll find lots of diagrams to help explain it.
Hope that helps.
Roger.
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