Standard deviation is an index of variability that statisticians can use to characterize the dispersion among the measures in a given population. It’s the measure of the spread of the data about the mean. Numerically, the standard deviation is the square root of the variance. Unlike the variance, which is a somewhat abstract measure of variability, the standard deviation can be readily conceptualized as a distance along the scale of measurement. (seehttp://www.robertniles.com/stats/stdev.shtml for a good non-technical explanation of Standard Deviation)
Other Definitions
Standard Deviation – The standard deviation of a probability distribution is defined as the square root of the variance (http://mathworld.wolfram.com/StandardDeviation.html)