Variance is a measure of how much a random variable deviates from its expected value. Defined for the random variable X by:
Var(X) = E((X-EX)2) =
= E(X2) - (EX)2
(so it might not exist, even if X has expected value).
Both lines are used as definitions, and it is hard to pick the one over the other. To see the equality between the 2 lines, just open brackets on the first, and use the fact that expectation is linear, and that μ=EX is some constant.
The square root of the variance is the standard deviation of the variable.