According to legend Bloody Mary is the ghost of an unhappy woman who either committed suicide due to having her baby stolen or was accused of murdering her children. Depending on the variation used this turned her spirit mad with grief or anger, and she would haunt the world via the use of mirrors (in an almost identical fashion to Candyman).
Known in life as Mary Worth it is traditionally said that "Bloody Mary" will appear if a brave (or foolish) soul chants her name three or more times next to a mirror in complete darkness at midnight. According to the variations of the legend above one is also said to be able to make the ghost appear via stating "Bloody Mary, I killed your baby" or "I believe in Mary Worth".
Of course anyone foolish enough to provoke Bloody Mary is said to pay the price, unlike many ghosts (who merely scare humans) Bloody Mary is said to be capable of physical harm and will either kill her victims via disfigurement, decapitation or scratching their eyes out. If she is in a "merciful" mood, Bloody Mary is said to simply turn her victim insane or (in rarer tales) she may take a fancy to someone and drag them into the mirror (presumably to the Other Side.)
Although the tales of Bloody Mary are dismissed as a modern fairytale of sorts by most people it is still a popular "game" amongst certain groups of people and may even be a rite of passage to some, a means of confronting one's fears or a way to play a mean prank on someone.