Why does a steady-state non-zero body yaw and/ or roll rate induce side force?
Let's say we have a thin, straight and rigid stick traveling in a 2D circular path. We will attach our reference of frame to the CG of the stick, aligned with its natural forward. If it has a forward speed of $u$ and the circular path has a radius of curvature of $R$, then it has a yaw rate, $\dot{\psi}=u/R$, all of which are expressed in the said reference frame.

At locations forward or aft of the CG, different parts of the stick will experience different lateral speeds due to the yaw rate, when measured using our reference frame: $u(x) = \dot{\psi}x$. The intuition is that the stick is spinning, so top and bottom will experience the largest speed while the centre will have none.
If you had attached a fin near the of the stick, then it will experience a side airspeed, effectively giving it an aerodynamic incidence angle. As a result, there will be aerodynamic forces and moments, simply from the motion of rotation.
From an analysis perspective, we usually don't re-calculate the effects on every surface due to local speed changes. Instead, the stability derivatives are measured in the body axis (well, usually in the stability axis but easily transformed to the body axis). So we can easily lump the sum of the aerodynamic effects of the individual portions into a single derivative with respect to the rate of rotation about that axis.