Roleplaying is a term which refers to the act of various people taking on the roles of characters, assuming their actions in a shared imaginary world either through assimilative actions, taking control of an avatar, or through verbal or literary descriptions. The result is an unscripted story being created, often in real time, with everyone participating to further the plot line.
Many times a roleplaying session will have either a set time limit, or a set number of sessions, at the end of which the story comes to some sort of discernable conclusion. These are called closed roleplaying sessions, because they have a definite and defined ending point.
The flip side of this is open ended roleplaying. This occurs when a world is allowed to persist continually, with players able to access it with their characters at will. One example of this would be the popular game “world of warcraft” which is available online, twenty four hours a day and seven days a week allowing for network time outs and technical glitches. Players can log on and further their own personal stories pretty much at will, which helps to slowly further the main story arc that the site is slowly pushing forward.
One of the properties often found in open ended roleplaying sessions is that they involve entire worlds, rather than just one predefined location, like a dungeon. Having that much space to spread out allows the characters to embark on a seemingly endless number of wild adventures, which can twist and complicate the plot of the overall story arc in enumerable ways.
It is also possible to use open ended roleplaying for table top exercises. The story merely does not have to end, and each session can build upon the one that came before it. The only problem is that if the story goes on for too long, the characters paths may divulge, making it difficult to keep up with what everyone is doing. Luckily the person running the game can then decide to either split the game into two boards, employing a second referee, or can simply guide the paths of the characters back, intertwining their lives around one another.
Open ended roleplaying is just one option when engaging in communal storytelling. It provides the widest range of choices for characters, and allows the story the broadest berth. However it can also make it harder to maintain focus over time, and so is not for everyone who likes to play.