Standard deviation is an important measure of spread or dispersion.
When comparing distributions, it is better to use a measure of spread or dispersion (such as standard deviation or semi-interquartile range) in addition to a measure of central tendency (such as mean, median or mode).
For example, the following two data sets are significantly different in nature and yet have the same mean, median and range. Some sort of numerical measure which distinguishes between them would be useful.
1, 7, 12, 15, 20, 22, 28
1, 15, 15, 15, 15, 16, 28
The standard deviation of the first set of data is significantly larger than the standard deviation of the second set of data (ie there is more spread about the mean in the first set of data).