Standard deviation is a mathematical measure which approximates the average deviation of any given data point from the mean of the entire data set. For example, if a data set of 100 has a standard deviation of 5 and a mean of 50, then on average no value will be outside the range of 45-55.
The calculation for standard deviation is simply the square root of the variance.
In finance, standard deviation is used to measure risk. If an asset has a return of 10% with a high standard deviation, then it is less likely that it will return that 10% consistently and is therefore more risky.