Destiny is a predetermined course of events; the path one follows, the choices one makes, one's life's purpose, until the day that he or she dies. All destinies are controlled by the Angels of Destiny, beings who maintain the Grand Design and the cosmic balance. Because of the sheer number of destinies in the world, there are various angels to help maintain them. Beings who exist outside of space or time, such as Cole Turner and Neena, are also beyond the reach of destiny.
While generally unchangeable, it is possible for an Angel to offer his or her charge to change their destiny. In 2003, the sisters were offered to change their magical destiny as a reward for vanquishing the Source of All Evil, and become mortals. Although Piper and Phoebe were willing to accept the offer, Paige was not. In this case, since the destinies of the charges were so closely tied, majority had to rule. Fortunately, the sisters eventually agreed to keep their powers in a unanimous decision after saving another innocent.
Notes and Trivia
The Angel of Destiny's comments in Witch Way Now? about the girls' success seem to imply that although destiny is predetermined, it is entirely possible that events do not come to pass when expected, or may even happen much earlier than thought, as with the Charmed Ones' vanquish of the Source of All Evil. This fact alone seems to imply that while destiny is predetermined, it is also mostly a general path that people follow, and not quite specific as to where and when it will be fulfilled.