Smithing Stones in Elden Ring are a consumable resource used to upgrade your weapons, increasing their damage. This is an essential mechanic if you want to progress through the game, but as you upgrade your weapons, you'll need to acquire superior forms of Smithing Stone to increase their rank, with the most powerful weapons earning a +25 rating.
Upgrading your weapons can therefore be pretty costly, and you'll need to acquire large numbers of stones, with Elden Ring Ancient Dragon Smithing Stones for the highest levely. And while basic Smithing Stones upgrade basic weapons, there are also Elden Ring Somber Smithing Stones which are used to upgrade the specialized unique weapons earned from bosses and so on. Make sure to check the attached guides for specific info on those!