When all of the requirements are met, you can Reforge Gear into a stronger version of itself.
When a Gear piece is Reforged, its stats will be reset. However, through Augmentation, they can then be raised higher than they could before Reforging. The appearance of the Gear piece also changes after Reforging.
However, Reforging requires materials that can only be obtained from special Monsters.
Once you Reforge, those materials will be consumed and cannot be used again.
Gold is also required to Reforge Gear.

[How to Reforge]
Tap [Gear] > [Reforge], and then tap on any Gear that can be Reforged.

[Confirming Materials Needed for Reforging]
Tap [Gear] > [Reforge], and then tap on any Gear that can be Reforged to view the materials required to Reforge that piece of Gear. *The materials required vary depending on the Monster and Gear.

[Caution When Reforging]
The + values attached to a material used to Reforge will not be passed onto the base Gear.
However, the + values attached to the base Gear will remain after Reforging.