These are notched boxplots. The standard boxplot summarises a distribution in terms of interquartile range (IQR) and median, with 'whiskers' extending to either the full range or some heuristic multiple of IQR after which "outliers" are plotted as points.
The notches show a non-parametric estimate of ~95% confidence intervals of the median. The reference most often given for these is "Variations of boxplots" by McGill, Tukey and Larsen (1978). A recent reference is Visualizing samples with box plots in Nature methods.
Most statistical packages will let you add these as an option when drawing boxplots, for example in R the
boxplot command has the argument
notch. Note that there are various subtly different methods of calculating the notches which may vary between implementations.