Definition:Variance/Discrete/Definition 1

Definition
Let $X$ be a discrete random variable.

Then the variance of $X$, written $\var X$, is a measure of how much the values of $X$ varies from the expectation $\expect X$, and is defined as:
 * $\var X := \expect {\paren {X - \expect X}^2}$

That is: it is the expectation of the squares of the deviations from the expectation.

Also see

 * Equivalence of Definitions of Variance of Discrete Random Variable