Dropped by the Orc King field boss, Jasper ore is on the same tier as Emerald ore in terms of strength and usability, but it's latent power is that of the earth Elemental, the major strength against electric-based enemies as well as the mysterious Energy Elemental.
Much to be expected at this point, Jasper ore is only meant for weaponry, and it cannot be fused into armor to strengthen it. Armor can be decorated, but no different properties would be applied other than a cosmetic difference.
As to be expected as well, Jasper Ore-based weaponry has storage of energy for releasing the elemental, the more used at one time the longer it takes to recharge the capacity.
More uses for Jasper ore will be more apparent as the game progresses.