I'll explain this for you.
Moderator's reports DON'T get responded to faster (which I earlier thought) but they get filed to a seperate section. Player Moderators can also hand out TEMPORARY 24 hour mutes. Occasionally when a player is being particularly defiant towards the rules, a mute is required so that other players can no longer see his or her text. A Player Moderator's mute is a safety precaution to help prevent the player in question from causing any more harm to themselves or others, as it will effectively stop any attempts to scam, advertise websites, or endanger others. Jagex Staff provide Player Moderators with muting guidelines, and mutes are quickly checked to ensure that they are correct. Any incorrect mutes are promptly lifted, and if a Moderator regularly mutes without proper reason, his or her moderator status will be removed. As soon as a Jagex Moderator checks the report, the mute is lifted and a subsequent punishment is then applied if it is needed. Players muted by Player Moderators are able to use quick chat.
Player Moderators have access to additional forums and the P-Mod Room, in which they can discuss moderator issues with other moderators and Jagex staff. They also have access to the Player Moderator Centre, which can be reached from within the Moderators article in the Game Guide. Jagex states that content discussed within these areas is strictly confidential, and any Player Moderator who reveals content within these areas will lose their moderator privileges.
The P-Mod Room is a special area within the game that can only be accessed by Player Moderators while a Jagex Mod is present. Only current player moderators can give the command to enter. According to Jagex staff, the P-Mod Room is "effectively a blank room that's a direct copy of an existing dungeon found elsewhere. That's to ensure that mods don't have access to anything that the rest of the community doesn't. I should also point out that it's not possible to practice skilling or anything while in the room as this could be considered an unfair advantage". In this quote, the "existing dungeon found elsewhere" is the Varrock West Bank's basement just stripped of most furniture and the wall and gate in the middle. The room is used for surgeries, which are scheduled question and answer sessions where Player Moderators ask for advice from the Jagex staff. All discussion during a surgery is strictly confidential. Before the December 2007 updates, surgeries would often be followed by a "Bot busting" session.
Hope this helped.