In roleplaying games, players create original fictional personae (i.e., characters) assume the roles of these created personae and act out the events of their day to day lives. Ultimately, roleplaying is about becoming other people in another world and weaving their life stories in a manner that is entertaining, meaningful, and worth remembering.
Think of the imaginary world that players explore as being a novel, the players as being authors, and their created personae as being pens - these characters are the tools that players use to express their creative vision within the imaginary world. Characters are the sole property of their creators, as pens are the sole property of their author, and the most valuable tool players have at their disposal.
Some roleplaying games utilize an individual referred to as the Game Master. This individual is, at best, an editor, not an author - they exist solely to make sure that the creative vision of the authors (i.e., players) remains consistent, never deviating far from the structure within which the authors have agreed to work (i.e., system, setting, social contract, etc) in order to create their magnum opus.
Other roleplaying games are truly collaborative, splitting the usual duties of an editor amongst the authors themselves, empowering them completely and facilitating the creation of unadulterated epics. Often, the output of such collaborative writing pools lacks the consitency of those works carefully edited by a single individual, but espouse a greater sense of mystery and wonder as a result.
[Edit: This is but one view of RPGs. Some view RPGs a method to explore pre-existing stories, as opposed to creating stories and, accordingly, assign much more power to the role of Game Master while simultaneously stripping some measure of power from the players. There's nothing wrong with this, mind you - it's just not what I want out of an RPG, thus it isn't the definition that I use to explain them.]