Definition:Sigma-Algebra/Definition 4

Definition
A $\sigma$-algebra is a $\sigma$-ring with a unit.

Thus, a $\sigma$-algebra is an algebra of sets which is closed under countable unions.

Also see

 * Equivalence of Definitions of Sigma-Algebra

Linguistic Note
The $\sigma$ in $\sigma$-algebra is the Greek letter sigma which equates to the letter s.

$\sigma$ stands for for somme, which is French for union.