A role-playing game usually has no one specific goal; rather it is made up of stories or quests that are of interest to the players. For example: The characters hear news of a captured princess and resolve to rescue her, or perhaps they have to thwart the plans of an evil overlord and thus save their families from certain doom. Game goals are often dramatic.
Most games maintain some level of continuity between their stories. Consider the two goals above: the princess might have been saved but what do the characters do with her now? Does she still have a father or a kingdom that wants her? Or perhaps the characters couldn't stop the evil overlord, what do they do now? Try again?