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 $\mathbf V$.
An axial vector is a vector quantity $\mathbf V$ which is not transformed to its negative when you reverse the axes of the coordinate system in which $\mathbf V$ is embedded.
The direction of $\mathbf V$ is determined by convention to be according to the right-hand rule.
Let $\mathbf V$ be an axial vector acting with respect to an axis of rotation $R$.
Consider a right hand with its fingers curled round $R$ so that the fingers are pointed in the direction of rotation of $\mathbf V$ around $R$.
The right-hand rule is the convention that the direction of $\mathbf V$ is the direction in which the thumb is pointing:
Also known as
An axial vector is also known as a pseudovector.
Rotation is an axial vector.
Angular velocity is an axial vector.
Angular acceleration is an axial vector.
- Results about axial vectors can be found here.