Refine is a feature of the N Terraria mod made by its developers.
Refining basically adds a feature which would be the next step after reforging a item.
Refining will add more % based modifiers to the already existing modifiers on a weapon, an extra one with +% chance as you upgrade it and upgrades to the armor.
The NPC that handles the refining is the blacksmith:
"The Blacksmith was found"
He is obtained by getting a gold or platinum bar. He can spawn during the day and night.
- When items are refined, they gain a "+1" next to their name, indicating the amount of times the item has been refined. As such, the number goes up as the item is refined, until it's refined ten times. Refining at this point causes the item to move to the next rarity tier, and get even more powerful. This continues until the item reaches (mod-added) Red Tier, which stops at +10. After this, the item will not upgrade any further.
-When you refine shields they get bigger defence boosts.
-Tools currently receive a MAJOR benefit from refining. For example: A Platinum pickaxe that is completely upgraded has a 235% pickaxe power and mines faster than a Picksaw, all with pre-hardmode materials and easily obtainable money from a merchant. (Subject to change in NT6)
-Weapons, armor, accessories (including wings), fishing rods and shields can be refined. Also things such as Arrows and Bullets may be refined as well up to a stack at a time. Accessories only appear to gain bonus speed (which has no effect, however). This might also apply to armor as well, but more testing needs to be done.
-It is unclear if refining ammo does more than increase the damage value.
These are examples of refined weapons, the number indicates the level of each and the red name which is the 2nd tier seen thus far: