PvP

PvP is when you and another player attack each other until one of you dies.

PvP is usually instigated when another player rings a Sinister Resonant Bell and enters your world, through a Chime Maiden, or when a player rings a Beckoning Bell.

As a Host

As a host, if you are invaded, your job is to defeat the invading player by any means necessary.
To avoid being invaded, or to avoid further invasions, defeat the Chime Maiden.

As a Summon

As a summon, your job is to protect the host, with your very life if need be. Defeating the invader is a goal now, to assure the safety of your host.
As with the host, kill the Chime Maiden to avoid an invasion, or to avoid further invasions.

As an Invader

Your goal is to defeat the host and any summons by any means necessary.