A supermoon is defined as a full moon that coincides (or very nearly so) with lunar perigee — when the moon arrives at that point in its orbit closest to the Earth.
Up until around 2011, this was usually referred to as a perigean full moon.  The term supermoon was first coined by an astrologer, who also claimed that full moons occurring at distances within 90% of the perigee distance can also qualify as a supermoon.  As a result, there can be more than one supermoon per — typically most years see three; the perigean full moon flanked by supermoons the month before and the month after.  Sometimes there can be four supermoons.  Rarely, some years can see as few as two or as many as five.
See this comprehensive listing of supermoons from 2000 to 2100 compiled by retired NASA astronomer, Dr. Fred Espenak.