Used in both mathematics and physics, the right hand rule is a mnemonic for specifying the direction of vectors in 3 dimensional space.
As an example, suppose we are looking down on the xy plane and want to specify the direction of the positive z axis using the right hand rule. Hold your right hand perpendicular to the xy plane in such a way that you can curl your fingers from the positive x axis to the positive y axis. Depending on how those axes are placed, your right hand thumb will either point into the xy plane or out of the xy plane. The direction your thumb points is the direction of the positive z axis.
Right handed coordinates