Variance is the average of squared differences from the mean. Standard deviation is the square root of variance, expressed in the same units as the original data, making it more intuitive for measuring data spread.
Population SD divides by N (all data points). Sample SD divides by n-1 (Bessel's correction) to provide an unbiased estimate of the population parameter when working with a sample.
Standard deviation is used in finance (investment risk/volatility), quality control (process capability), education (score distribution), research (data reliability), and many other fields. Lower SD means data is more concentrated around the mean.