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This is with regards to adiabatic magnetisation.

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If the magnetic dipoles in a material are ordered, the material has a lower entropy because there are many fewer ways how the spins may be oriented if most of them (or all of them!) are required to be aligned.

Such an alignment also reduces the heat capacity because before the dipoles got aligned, the orientation (direction) of each dipole was a degree of freedom that was storing something like $O(kT)$ of energy where $k$ is Boltzmann's constant and $T$ is the temperature in kelvins.

However, when the dipoles are kept aligned, the direction is no longer variable so the heat capacity from each dipole decreases by $O(k)$ or so, or $O(R)$ if expressed per mole.

It's a similar difference as the heat capacity of monoatomic vs diatomic gas, which carry $3kT/2$ vs $5kT/2$ per molecule, respectively. ($3/2$ is from 3 linear momenta and the extra $2/2$ is from the longitude and latitude remembering the rotational motion and/or direction of the diatomic molecule.) Note that the diatomic gas has a greater energy per molecule which scales with $T$, and therefore also steeper dependence of the energy on the temperature (the capacity is $5R/2$) because the energy may also be stored in the random rotations of the diatomic molecule that don't exist for the monoatomic molecule. The random chaotic thermal rotation of the dipoles is analogous to the random rotation of the diatomic gas molecules and it becomes banned or indistinguishable for monoatomic gas as well as the magnetic material with aligned spins which is why the heat capacity decreases analogously to the decrease from $5R/2$ to $3R/2$ in the transition from a diatomic molecule to a monoatomic one.

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