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