Binning groups pixels together which has the effect of making the group appear as a bigger single pixel as shown in figure 1 above (Templeton & Beck 2014). Binning is done to decrease the resolution:
So by increasing the pixel size while keeping the focal length constant, the resolution goes down. This might seem backwards, but lower numbers imply higher resolution since less of the sky is "landing" on each pixel creating a sharper image. The benefit of binning is that you gain better sensitivity so you can do shorter exposures (Templeton & Beck 2014). The drawback is that you do lose some resolution so you have to be careful not to blend close by stars together if you are trying to do accurate photometry (Templeton & Beck 2014). Another important thing to remember is that you have to redo all of your calibration frames and test the linearity for each set of bins (Templeton & Beck 2014). In other words, a dark frame at 1x1 binning is not equivalent to a dark frame at 2x2 binning.
References
Templeton, M. & Beck, S. (2014), The CCD Guide to Photometry Version 1.1, Cambridge, MA
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Nice read @ptsouth97
This may be true theoretically but in practice, it is unfortunately not. It may change the area of a pixel and with this its ability to catch photons, but the area of the whole sensor is not changed at all. You need to see the whole sensor area, not the pixel alone.
So sensitivity is the capability to catch photons and this can only be increased by decreasing the focal ratio of the optic, by increasing the area of the sensor or by increasing the quantum efficiency of the sensor.
For me, the benefit of binning is to reduce data where it is not needed. Maybe in the RGB channels of an LRGB image. Humans eyes have the "highest resolution" in contrasts, so the L channel should never be binned.