Definition:Axial Vector/Definition 1

Definition
An axial vector is a vector quantity $\mathbf V$ used to specify action which takes place around an axis of rotation.

In this case, the $\mathbf V$ is considered as acting parallel to the axis about which $\mathbf V$ acts.

As for a polar vector, the length of $\mathbf V$ indicates the magnitude of $\mathbf V$.

The direction of $\mathbf V$ is determined by convention to be according to the right-hand rule.

Also see

 * Equivalence of Definitions of Axial Vector