As a teacher of junior maths and Maths in Society, I used to think that a histogram was a rather trivial statistical object, sort of a bar graph with the gaps removed to save space. A modern data-centred approach to statistics starts with viewing the data in a variety of ways. Features of interest to a statistician are the overall shape of the data, symmetry, the location and the spread, existence of outliers and evidence of clusters or gaps. A histogram with a scale on the horizontal axis is generally useful for showing all of these features, though for some distributions the features of a dataset can be disguised or distorted due to a particular choice of bin width. One application of the humble histogram is determining if a set of data is approximately normally distributed, though a histogram is most effective with for this purpose if the dataset is large.
Normality is a pre-condition for certain analyses of data, including many hypothesis tests.
While there are formal tests of normality, often a quick look at a histogram of the data is sufficient. And no statistican would rely strictly on formal tests without viewing the data also. Compared A histogram shows much the same information as a stemplot, though for a given dataset one or the other of these methods of displaying the data may be preferable. Bin Width Statistics computer programs and graphical calculators will generate a default histogram if bin width or the number of bins is not specified. It is interesting that there is no clear winner in the choice of algorithm used for choosing the number of bins or the bin width.