Battle Points (or abbreviated as BP) are a form of currency won by Trainers who can defeat other Trainers in specific battling areas such as the Battle Frontier or the Battle Tower. The Battle Subway also awards you with these after a 7 win streak. Battle Points can be traded for rare items.
The first Battle Points that a player could earn in Emerald came from Scott, who would give them away to the player on the first visit to the Battle Frontier, depending how many times he and the player interacted throughout the game.