Ability awakening refers to the act of enhancing abilities to increase their potential effects such as damage, passive skills, and so forth.

Awakened abilities are displayed with a different color icon on which their awakening level is displayed.

You can awaken abilities by going to Units ► Awaken Abilities ► then choose a unit with an awakenable skill.

Awakening abilities requires different materials depending on their type (white/black/green magics, ATK/DEF types, healing/support types, and so forth).

You can farm materials by going to Vortex of Desires ► Chamber of Gems.