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PvP is the game action of eliminating another player's character from the game, either through death, having a contract put out them or otherwise forcing them to give up freelancing.
PvP is a valid action in the game, but it is discouraged. It should be considered a last resort in dealing with a character you disagree with and there are consequences for doing so.
You can kill another character by using the Coup De Grace call on them when they are on the floor with other injuries. This is the only way to guarantee someone is dead. Simply shooting them gives them a chance to survive.
If someone does not have the first aid materials to pick themselves up after a fight then choosing to leave them to die is a valid option. This does still count as a PvP action but it does not attract the same level of consequences.