What information does a Box Plot provide that a Histogram does not? Histograms give a good sense of the distribution of a variable. Box plots attempt to do the same thing however, don't give as good of a picture of the distribution of this variable.
I don't understand why people use box plots. Histograms are better in every way. Is there a reason I would use both of them?
The only thing I think that box plots provide is: outliers! It tells us which observations may be outliers.
 A: *

*If I show you a histogram and ask you where the median is, you might be quite some time figuring it out... and then you'll only get an approximation to it. If I do the same with a boxplot you have it immediately; if that's what you're interested in, boxplots obviously win.


*I agree that boxplots are not as effective as a description of the distribution of a single sample, since they reduce it to a few points and that doesn't tell you a lot.
However, if you're comparing many dozens of distributions, having all the details of each may be more information than is easily compared -- you may want to reduce the information to a smaller number of things to compare.


*If more information is better, there are many better choices than the histogram; a stem and leaf plot, for example, or an ecdf / quantile plot.
Or you could add information to a histogram:



(plots from this answer)
The first of those -- adding a narrow boxplot to the margin -- gives you any benefits to be gained from either display.
A: The fact that box plots provide more of a summary of a distribution can also be seen as an advantage in certain cases.  Sometimes when we're comparing distributions we don't care about overall shape, but rather where the distributions lie with regard to one another.  Plotting the quantiles side by side can be a useful way of doing this without distracting us with other details that we may not care about.
A: In the univariate case, box-plots do provide some information that the histogram does not (at least, not explicitly). That is, it typically provides the median, 25th and 75th percentile, min/max that is not an outlier and explicitly separates the points that are considered outliers. This can all be "eyeballed" from the histogram (and may be better to be eyeballed in the case of outliers). 
However, the much bigger advantage is in comparing distributions across many different groups all at once. With 10+ groups, this is a tiring task with side-by-side histograms, but very easy with box plots. 
As you mentioned, violin plots (or bean plots) are somewhat more informative alternatives. However, they require slightly more statistical knowledge than the box plots (i.e. if presenting to a non-statistical audience, it may be a little more intimidating) and box-plots have been around much longer than kernel density estimators, hence their greater popularity. 
A: Bar plots provide only the range of frequency of observations while box plots are better in telling where several parameters of a distribution lie, example mean and variances that bar plots cannot. Box plots are thus used as an effective comparative tool if one has several distributions.
