Emergent Gameplay is a broad term used by Jagex that refers to in-game activities developed by players. Emergent gameplay revolves around the use of in-game content in ways that were not specifically intended by Jagex when they created the content.  
A wide range of activities are included within the scope of emergent gameplay. Some of the more prominent examples of this include clans, scavenger hunts, hide-and-seek games, and role-playing games.
Emergent games are normally hosted inside a POH, The Grand Exchange, the square in Varrock and other popular places. They are normally played in clans.