All the new units in this latest batch have a passive ability that allows them to acquire new skills by using some they already know. These new skills last for the rest of the battle. If you've used Rikku its kinda like that but no turn duration and out of your control.

The simplest example would be Katarina. She starts with one skill (払い抜け) and can unlock two skills (逆風の太刀 & 地ずり残月). When she uses 払い抜け there is a chance that she will use 逆風の太刀 instead. This is called "Sparking". Once she "Sparks" the new move, it's in her moveset (for that battle). Now using either 払い抜け or 逆風の太刀 will have a chance to "Spark" into 地ずり残月, her final skill. Now her moveset is complete and there's no more sparking.

Each of these units has a set of moves like this. Using any of the moves in the set will have a chance to "Spark" into a skill until you have the entire set. Also the moves can have different chances for unlocking the next.

Example: Harrid's かすみ二段 has a 60% Chance to Spark into 疾風剣, while his 分身剣 only has a 30% Chance.

You can find more details for each unit on their wiki page.

• Julian: https://www.reddit.com/r/FFBraveExvius/wiki/units/665
• Katarina: https://www.reddit.com/r/FFBraveExvius/wiki/units/667
• Harrid: https://www.reddit.com/r/FFBraveExvius/wiki/units/669
• Robin: https://www.reddit.com/r/FFBraveExvius/wiki/units/672
• Demigod Adel: https://www.reddit.com/r/FFBraveExvius/wiki/units/675