Perks are characters' passive skills that have a certain chance of being activated during battle when the given perk is in your equipment.
Special moves are active skills that can be used during battle by moving towards your opponent + arm/leg strike when the special move is in your equipment.
After gaining a perk or special move, you unlock the ability to raise the perk's level, special move's level, and also improve the rarity of a special move by using certain resources:
Umbracite can be used to increase the level of perks.
Chrysonite is for increasing the level of special moves.
Magmium is for upgrading the rarity level of special moves.
These resources can be gained from Void Chests, as well as from rewards won in Raids mode.
Perks and special moves can be obtained from Void Chests. Perks and special moves are also periodically available in the rewards for other in-game activities.
If you receive a card that is already in your collection, you will get resources for upgrading it.
Find out more about how to unlock Void Chests in this article:
How do I open void chests?