Binning means grouping a continuous variable into discrete categories. It is particularly used in reference to histograms, but could also be used more generally in the sense of coarsening.

Various rules have been proposed to choose a number of bins in a histogram; as is often the case, it is a tradeoff: With too many bins, the histogram will be very bumpy and reliant on the particular data set. With too few, necessary detail is lost. This is discussed in this thread

One problem with histograms is that different binning can result in histograms that appear quite different.