The specific angular momentum (J) of an orbiting body is its angular momentum divided by its mass, i.e., the angular momentum per unit mass.
J = L/m
The decision as to which mass may depend upon the use to which it will be put.
Angular momentum is a "momentum" associated with rotation and is represented as a vector along the axis of rotation, with a vector magnitude representing the degree/amount. For a point circling an axis, it is:
L = rmv
Conventionally, the choice of directions along the axis uses the right hand rule. Following this convention allows the vectors to be added to calculate the angular momentum of multiple points fixed to each other as a rigid structure. The "right handedness" in its definition is an arbitrary choice, but makes things consistent.
Angular momentum is conserved. If you begin spinning yourself, the Earth's spin is very slightly modified in the other direction so the total angular momentum including you and the Earth has not changed.