What advantages can you gain from battle power points:

Quick Levelup:
You will gain extra exp. from your battle power points when killing monsters. You may hover your mouse cursor on the monster to check how many extra exp. points you will acquire.
Defeating some bosses
There are some bosses with battle power points too. You have no chance to defeat them unless you have higher battle power points than they do.
Damage cap:
It`s mainly for PK. If you have higher battle power points than the attacker does, there will be a cap on the damage that he can deal to you. If your battle power points are much higher than the attacker`s, there will be a blue shield in front of you when he is attacking you. If the shield is red, it implies his battle power points are close to yours.


How to calculate your battle power points?

Character level:
One level up, one more battle power points.
Rebirth times:
5 battle power points for the first rebirth, 10 battle power points for the second rebirth.
Quality of equipment:
4 battle power points for one piece of super gears
3 battle power points for one piece of elite gears
2 battle power points for one piece of unique gears
1 battle power point for one piece of refined gears
Sockets of equipmentt:
One battle power point for each socket.
Super gems:
One battle power point for each super gem.
Bonus status of equipent:
1 battle power point for each +1 item
2 battle power points for each +2 item
3 battle power points for each +3 item
4 battle power points for each +4 item
5 battle power points for each +5 item
6 battle power points for each +6 item
7 battle power points for each +7 item
8 battle power points for each +8 item
9 battle power points for each +9 item
Others

Side note: The left-handed weapon will not be counted. And you will gain double battle power points from those two-handed weapons, BackSwords and Bows.