I assume it's points for winning battles at the Battle Maison/Resort, but, 2 things, at the battle Resort, is it still limited to Pokes below lvl 50, and how much bp to you get depending on the battle?(The reason I'm asking is because I need an Assault Vest for my future Rhyperior.)
Every battle that you do at the Battle Maison will give you BP, or Battle Points. Usually after a battle you get 1 or 2 BP, but the more battles you do in a row the more BP you can get per battle. After Battle 20 with the Battle Chatelaine, you can start gaining 3 or 4 BP per match.
Any Pokemon can be used as long as they aren't "big legendaries" no matter what level. If they are below Level 50, they will remain at their level.
Source: experience