Badge Points, also known as BP, are a recurring feature in the Paper Mario series. Badge Points enable Mario to equip badges, with each individual one coming with a set number of Badge Points needed to be used.
In Paper Mario series

In Paper Mario, at the beginning of the game, the amount of Badge Points Mario possesses is three and goes up by three every time he levels up and chooses to upgrade BP. Mario can acquire a maximum of 30 Badge Points.
In Paper Mario: The Thousand-Year Door, Badge points work similarly to those in the previous game, however Mario can reach a maximum of 99 instead of 30. Additionally, Mario's partners can use partner badges, but they take from Mario's BP to use them.