Battle Points also known as BP, are a currency in Doodle Army 2. They are used to buy the special upgrades in the store.
These Battle Points are gained via killing other players in online matches. For example, you get 3 kills in a match, you will get 3 Battle Points. You lose 1 Battle Point for each suicide but if you have more suicides than kills then you will get 0 Battle Points.
Points (minus suicides). 9 Team kills do not count as actuall kills, so you won't get 9 BP unless everyone else on the team doesn't kill anyone for the duration of the game..
You can also buy them in the App Store/Google Play Store.