A frame usually refers to a coordinate system that is moving in space. It can translate and rotate, and it is attached to ta rigid body. This way the inertial properties of the body remain fixed on this coordinate frame.
In the example below the reference frame $A$ has origin $\vec{r}_A$, and unit direction vectors $\hat{x}$, $\hat{y}$ and $\hat{z}$.
In this reference frame, the mass moment of inertia $I_{\rm xx}$ about the $\hat{x}$ direction, for example, is fixed as the body moves through space.
A frame also refers to the extented body which represents what would happen to the particles of the body if they extended beyond their physical limit and outwards to infinity. So their velocity will increase with distance as the body rotates.
The unit directions of a reference frame define the rotation matrix that is used to transform vectors from the local coordinate frame to the world coordinate frame.
$$ \mathbf{R} = \left\{ \matrix{ \hat{x} & \hat{y} & \hat{z} } \right\} $$
Finally, the inertia tensor from the reference frame $\mathbf{I}_{A}$ (which is constant with time) is transformed to the world coordinate system (where the rest of the equations are described) by the congruent transformation
$$ \mathbf{I} = \mathbf{R} \, \mathbf{I}_A \mathbf{R}^\top $$
The above is a 3×3 matrix equation, with ${}^\top$ being the transpose operator.
