In all open world PvP areas, players can kill enemy NPC or complete some objectives to gain pvp points. You have to walk/run back to base to turn it in. The more points you hoard up before you turn in, the better reward you will get. However, if you are killed by opposing player before you turn with BNS Gold, they will take ALL of your points. The reward for racking up a lot of point at once is quite lucrative. This will be the biggest incentive for players kill each other during open world PvP.
Soul stone and Moon stone are mostly acquired in open world PvP where you compete with the opposite faction for resources. These stones are used in crafting and upgrading gear, so they are very valuable (and sell well). You cannot turn off PvP while doing these quests or your progress is reset to get BNS Gold, so when you start doing the quest, you need to commit until you’re done. (as with most objective-based PvP, people will trade wins and avoid unnecessary fighting unless one side has a number advantage to bully the other)
In some versions of the game, there is also large-scale PvP contests, where participating players go into a mega instance and compete in a much more heated battle. However, many big guilds in servers end up monopolizing these and just trading wins with each other.