Ok, first it's important to distinguish between a sample and a population.
Imagine you're interested in 100 people's height, the population is all 100, but a sample is any subset of these. Because the sample is always less and might not be representative it has a higher error associated with it.
standard deviation of population (or variance squared)
=squareroot of (((sum of each data point - mean) squared)/N).
standard deviation of sample (or variance squared)
=squareroot of (((sum of each data point - mean) squared)/(N-1)).
The reason you take the square root is so the units of the error are the same as the units of the mean so you can say.
height = 1.8 +/- 0.25m instead of height -1.8m +/-0.05 m^2
I hope this helps