Overkill
From Final Fantasy Wiki
Overkill is a game element in Final Fantasy X that occurs when the character defeats a fiend or other enemy with excessive force. When this occurs, the player will be notified by a symbol listing the term before the fiend dissipates into pyreflies. "Overkilled" enemies are nearly always worth more AP, and may result in more Gil and better items. For example, the Area Creation Don Tonberry will drop three Farplane Winds or a Dark Matter. If Don Tonberry is Overkilled, however, then he will drop six Farplane Winds or two Dark Matters.
It is a good strategy to always strive for Overkills, as the extra items and AP will make your party stronger, which will make subsequent overkill easier to get.
