In principle, it is relevant also for gases or liquids, but on Earth their mass distribution is almost homogeneous.
In astronomy mass distribution has decisive influence on the development e.g. of nebulae, stars and planets.
The mass distribution of a solid defines its center of gravity and influences its dynamical behaviour - e.g. the oscillations and eventual rotation.
The mathematical modelling can be done by potential theory, by numerical methods (e.g. a great number of mass points), or by theoretical equilibrium figures.
Rotating solids are affected considerably by the mass distribution, either if they are homogeneous or inhomogeneous - see Torque, moment of inertia, wobble, imbalance and stability.