Each unit has several types of abilities: Basic, Special, Leader and Unique. The Basic ability is a simple attack that does not have a cooldown. Special skills are different for each character and always have a cooldown. Note: The special abilities of certain units work in synergy with other characters, e.g. by summoning them to assist. Leader skills are the bonuses that a character gives to a team while in battle, if they are currently in the first place in the squad. Unique skills are passive skills that directly affect a unit or a team - if, that is, the Unique ability is associated with a given character category.
Units with more skills have them blocked at the very beginning. Upgrading your character to another gear level will make them available. To improve your ability level use Ability Material, which is available in the Ability Mats Challenge, in some of the battles (e.g. Cantina Battles) and which can also be bought in some stores for the currency earned in the game.
The maximum level of development of most skills is level 7, but you can unlock characters who have level 8 skills. Advancing to level 8 is extremely costly (requires Zeta materials), but the unit gains a huge advantage on the battlefield.