Basically a forum RPG is an RPG without limits. The game could branch situations and events far beyond the capability of a programmed game, where the walls are set in stone. (if that makes any sense)
The whole game is centered around players participating in RPs. (Role Plays/Quests/Scenarios/Adventures/Whatever...) RPs can be created by both Dungeon Masters (Admins of the site) and players. To create your own RP you just start a new topic with your RPs name in the title and list any points of interest in the first post, for example, the max amount of players you want to participate, or the general plot outline. (If you have any at all that is. An RP might start with a player going to the shops to buy a new weapon and end with a gang of players slaying a dragon!)