Sorcery Card's Refinement Rank increases the potency of the sorcery card's effect.
You can increase the Refinement Rank of a Sorcery Card by consuming a duplicate of the same card to increase it's power.

i.e. Dark Sacrifice Refinement Rank can be increased by consuming a copy of the Dark Sacrifice in order to increase the Refinement Rank by 1. When increasing the Refinement Rank of Dark Sacrifice it will increase the Sorcery Card's Effect Increased Max HP and Damage bonus granted after Sacrificing HP.