Original: It is a misconception that angular momentum is always about the same axis as angular velocity. Sometime this may not be possible, in these cases the angular momentum component along the axis of rotation is the product of angular velocity and moment of inertia about the given axis of rotation.
Simplified: In particular, if a point mass rotates about an axis, then the angular momentum with respect to a point on the axis is related to the mass of the object, the velocity and the distance of the mass to the axis.