Starting at level 30, you will become eligible to take part in player vs player combat (PvP). On a PvP server you will be able to attack other players - as well as be attacked yourself - at any point in time when you aren't in a safe zone. Safe zones typically include all outposts, as well as the immediate vicinity of a teleporter.
PvP settings can be found in the upper left hand corner underneath your HP and MP bars, and can be accessed by clicking the small icon of the crossed swords. From the menu that appears, you can change how you interact with other players in terms of PvP - such as being able to automatically attack other white named players, but making it impossible for you to attack a guild mate.
PvP on a PvP oriented server is unconditional. This means that as soon as you reach level 30 on a PvP server, you are irreversibly flagged as being a viable target for attack in the field. Make sure that you are comfortable with being able to be attacked by other players at any time in the field before selecting a PvP server to play on.
Penalties upon dying in PvP range from nothing to dropping equipped items and inventory items, as well as losing maximum durability on your gear. The more people you slay, the darker color of red your name will get. The darker the color, the more severe penalties you will experience when killed in PvP.
Wrath Awaken Edit
Also at level 30, you will gain a skill called Wrath Awaken. This skill is aimed towards use against other players and will vastly increase your damage against players for a short period of time. You can recharge your wrath by gathering the orbs that fly off of players during a fight. Keeping your wrath skill operational is an important part of surviving a PvP encounter.
Other forms Edit
Besides open world PvP, where players can fight out in the field, there are many other types of PvP combat. There are duels (where one player fights another) and guild wars (where two guilds fight each other in an organized fashion).