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Hardware binning is when you take a grid of pixels and sum them before reading it out. The point of this is to reduce read noise. If you do 2x2 binning it means you're summing a grid of pixels, two wide and two high, into one before reading it out, so you get 1/4 the read noise. 3x3 = 1/9th etc.
People typically bin the colour exposures when shooting mono LRGB because you don't need as much resolution in this case as your resolution comes from your luminance frame.
Focal length can definitely contribute to the decision to bin or not. For instance I have an ED80 and an Atik 314L+, which is already undersampled. When binning, I lose even more resolution in stars and it can create some bad artefacts around them.
If you were largely oversampled you could bin without a significant loss of resolution, thus reducing your read noise.
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