Roughly the arithmetic average distance of the observed values from the mean. It is the square root of the variance, and represents the spread of a distribution. Its advantage over the variance is that it is expressed in the original measurement Units (the variance is expressed in squared units). The standard deviation of a population is represented by the lower case Greek letter 'sigma' (?). The standard deviation of a sample is represented by the lower case Roman letter 's'.
When the sample standard deviation is used to estimate the population standard deviation, the divisor in the formula is (N-1), to reflect the degrees of freedom left over (from N) after estimating the mean.
NIST Statistics Handbook: Measures of Scale - http://www.itl.nist.gov/div898/handbook/eda/section3/eda356.htm#VARIANCE