From Bulbapedia, the community-driven Pokémon encyclopedia.
Battle Points, or more often known as BP, are a special sort of currency in the Pokémon world that can be won as a prize for defeating Trainers in specific battle areas. They can be traded for many rare items.
When the Battle Tower was first introduced in Pokémon Crystal, each time a group of seven trainers was defeated, the attendants would award the player with a five status enhancing items at random, such as HP Up. The difficulty of winning in this first instance of the Battle Tower made acquiring large numbers of status-enhancing items expensive without cheating. In Pokémon Emerald, with the first sighting of the Battle Frontier, the concept of Battle Points was introduced instead.
The first Battle Points that a player could earn in Emerald came from Scott, who would give them away on the player's first visit to the Battle Frontier depending on how many times he and the player interacted throughout the game. After this, more could be won by challenging, and defeating, the various facilities. These could, in turn, be exchanged for rare items for a secret base or even moves that could be tutored to a Pokémon.
In Pokémon Diamond and Pearl, the concept was retained, even though the battle arena was restored to merely a Battle Tower. This time, EV-enhancing items were included, as well as rare evolutionary items. The Battle Frontier in Platinum also features this.
BP are awarded at the Battle Frontier in Johto as well. In addition, a limited amount of BP can be awarded once per day at the Trainer House. The Frontier Access features shops similar to the previous Battle Frontiers, where BP can be cashed in for items and moves.
The concept was retained in Pokémon Black and White, in the Battle Subway. The purchasable items are very similar to those in Generation IV, however, nearly all purchasable items are only obtainable here, and Generation V items were added. Also, the price of TMs went down, despite the fact that they are only obtainable once and the price of TMs in Poké Marts went up.
The Poké Coupons of the console games Pokémon Colosseum, Pokémon XD, and Pokémon Battle Revolution follow a similar concept. The prizes one can purchase in one game are usually similar to the prizes one can purchase with Battle Points in the game's respective handheld version.