Battle Points

Points
Battle Points, usually shortened to Points or simply P, acts as experience awarded to players after completing a multiplayer match. These count towards the player Inkling's level.

Use of Points
Points are primarily used to level up the Inkling. Points are also converted into cash, you may use the cash to improve your gear (such as clothes, shoes, and headgear) or buy weapons to increase your gameplay style

Each time you level up the Inkling you improve your choice of weapons and gear, each time the gear switches from each day you log on. Such as you see a "Varsity Jacket" and now you see "Pirate Tee" the next day.

Earning
Players can earn points in Turf War, Splat Zones or by fulfilling amiibo challenges. Splat Zones is for level 10 and above, once you unlock that level 10 you can play the mode Splat Zones

In Turf War, points are earned by covering ground. The more ground covered, the more points earned. A bonus 300 points is awarded to each player on the winning team if you are on the losing team however, you will still be rewarded with the points you earn in Turf War but, without the bonus of 300.

In Splat Zones, points are earned by knocking out the opposing team or by being the team with the least time on the clock when the match ends. Bonus points are earned by a "knockout." A knockout is when a team earns the 100 points needed to basically win the whole Splat Zone game. Even if there is no knockout, the team with the least amount of points in the mode Splat Zones will win the game.

Some more info about Modes in Splatoon there will be a new mode called Tower Points or something like that, added in August (exact date not known.) The info I know that there will be a tower that the opposing team and the team you are on have to claim the exact tower. The person on that tower will be the main target for the opposing team, so with that burden your allies will have to protect you so you can go to the point to win the game.