A Supermoon, or perigee moon, appears when the full or new moon implements its closest fly-by of the Earth, making it look much greater and brighter than it normally does. When in perigee (the closest point), the moon is 360,000km away from us, about 50,000km closer than when it is at its apogee (the furthest it gets from Earth).
Comparing to the other celestial events, Supermoons are rather common; they generally occur about once a year, though there were three during the last summer, and there will perhaps be around six in 2015.
Full and new moons frequently cause spring tides. Hence, those who live on the coast might experience higher than normal tides throughout these time-periods.
For centuries, legends have held that full moons, as well as Supermoons make people lose their minds. Full moons have been associated in popular culture with a rise in suicides and even epileptic seizures. Although there is a little scientific evidence backing such beliefs up, the moon is a powerful body; as mentioned above, its gravity tugs on our oceans controlling tides, and its light thought to impact ancient animal behaviors. This can to some extent explain the strange phenomena, such as lunacy, sleep deprivation, deviant behavior, etc. observed during the Supermoons.