The Hellfire Forge is a device added by Blood Magic for Minecraft 1.8.9 and above. It is needed to craft recipes requiring Will, which requires Demonic Will or a Tartaric Gem in the right slot that has enough default will to meet the required minimum will. All recipes are shapeless, and ingredients can be in any slot. The drain amount will be subtracted from the stored will. The Demonic Will/Tartaric Gem will not be lost. Both minimum and drain will amounts can be seen in NEI/JEI when hovering over the arrow.
A second use for the Hellfire Forge is filling Tartaric Gems. A Tartaric Gem in the right slot will drain from the aura in it's chunk. For example, melting Corrosive Will Crystal inside a Demon Crucible will fill the chunk with corrosive will, which will then fill the Corrosive Tartaric Gem inside the forge.