From the game's encyclopedia
Battle Advantage makes one side in Battle do more damage. The higher the Advantage, the more damage the Soldiers will do.
Battles often start with one side having a higher Advantage based on Terrain and the Martial Skill and Commander Traits of the Commander. Either side may then gain additional Advantage from Commander Rolls.
The game's text for patch 1.20.1.2. Words in blue are entries of the encyclopedia: hover one to read it, as in the game.
Battle Advantage is an entry of Crusader Kings III's in-game encyclopedia. The game explains it: "Battle Advantage makes one side in Battle do more damage." The game also links it as Advantage. Patch 1.20.1.2, from game/common/game_concepts/00_game_concepts.txt and game/localization/english/game_concepts_l_english.yml.
Source: game/common/game_concepts/00_game_concepts.txt, game/localization/english/game_concepts_l_english.yml and the English localisation, Crusader Kings III 1.20.1.2.