Arcane is one of the eight main attributes in Elden Ring that players can spend runes on to level up, increasing the stats effectiveness and influencing their relative secondary stats. It is not an obvious stat and is not considered in many spells or weapons, but it is still an important stat and is necessary for using some of Elden Rings best weapons. The primary function of the Arcane stat is governing item discovery, which influences how frequently normal enemies drop items after being killed. In addition, leveling up Arcane also increases resistance to Holy damage and resistance to buildup of the Death Blight status condition.
Arcane affects Holy Defense, Vitality, and certain Sorceries and Incantations. It is also one of the primary ways of increasing the Discovery stat, which increases the chance of items dropping from enemies, including making rare drops less rare. There are 15 different weapons in Elden Ring that scale off the Arcane stat, and most of the Incantations associated with Arcane are Dragon Communion Incantations, obtained by beating bosses like Flying Dragon Agheel, with the remainder being associated with blood loss buildup.
In terms of lore, Arcane in Elden Ring represents personal power in a raw sense, and it combines unorthodox and shunned aspects of Elden Rings world, which bleed falls under. It is associated with primal/natural forces and secret arts, including pentagrams and blood sacrifices. Intelligence is astronomy, faith is from the gods, and Arcane is primal/natural forces.