The right hand rule is a rule to determine the sense of a vector perpendicular to two vectors A and B. If you curl the fingers of the right hand in the direction from A to B along the smaller angle between A and B than the direction of C is pointing in the direction of your extended thumb or the direction in which a right-hand screw would move. If the direction of the movement from A to B is counterclockwise this direction is out of the plane formed by A and B and otherwise into the plane.

More general any ordered triple of vectors $(\vec u, \vec v, \vec w)$ with a common origin in $\mathbb{R}^3$ is a right-handed triple if the vectors are not in the same plane and the shortest turn from $\vec u$ to $\vec v$ as seen from the tip of $\vec w$ is counterclockwise otherwise the triple is a left-handed triple.

A three-dimensional coordinate system in which the vectors formed by the positive axes satisfy the right-hand rule is called a right-handed coordinate system, while one that does not is called a left-handed coordinate system.