Partying someone allows you guys to fight something while not being to hit each other, or if you want to, you can.
There are 2 types of "partying". Short-term and Long-term.
Being in a party automatically puts your "Party PVP" on off which you can turn on if you want to, but it will reset to off whenever you leave the game.
Being in a party also shows you the icon of party members of your on the map which you can turn off if you want to, you can also turn off your own icon if you want to.
You can also leave your party if you're a member. But if you're the party owner, you need to transfer your party ownership before leaving.
You can kick members (both long-term or short-term).
You can send party invites to players in the server.
Allows you to party someone temporarily. This will not save even if you or they leave the game.
Allows you to party someone which will save even if you leave, and if they join the game, they will be in the party automatically.
Having someone in your party will also show their current game status, which will be one of the 3 below:
Online (In SF, but a different server.)
In-game (Currently in your server.)
Offline (Not playing SF.)