The term 'narrative battle' describes any battle that allows players to explore the background by adding new rules to the game or by foregoing rules that seem restrictive in the circumstances. Of course, there is nothing wrong with simply fighting a battle for the sake of it – the game is there to be enjoyed in all its forms, and it can be argued that any game has a degree of narrative behind it as almost all players will imagine the action unfolding in cinematic scope within their mind's eye. A narrative battle is one that expands upon this, drawing both players into a shared story.
This can be done in a number of ways – by adding a story that sets the backdrop for the forthcoming battle, by adding scenario special rules or victory conditions (be they drawn from another scenario or source, or be they especially written by the players) that make the characters, armies or environment better evoke the story. In this way the battle itself completes the 'tale' begun by the scenario.