Soul Essence and Rare Soul Essence are materials necessary for leveling up activated Special Traits. These Traits are special abilities and separate from Basic Traits which were acquired through Limit Break.
Special Traits include increases in Lethal Damage, Counter Rate, Debuff Resist Rates etc.
In order to activate Special Traits, your Hero must be level 34.
How to unlock a Special trait
Slots for Special Traits must be unlocked using Transcender Fina. A maximum of 3 Special Traits can be activated per Hero. After a Special Trait has been activated, Traits can be leveled up using Soul Essence & Rare Soul Essence.
Leveling up a special trait to level 30 requires 8,700 Soul Essence & 2.2 million gold. If you're applying a special trait to a special hero, 348 Rare Soul Essence are also required.