The name SuperMoon was coined by astrologer Richard Nolle in 1979, defined as:
|“||…a new or full moon which occurs with the Moon at or near (within 90% of) its closest approach to Earth in a given orbit (perigee). In short, Earth, Moon and Sun are all in a line, with Moon in its nearest approach to Earth.||”|
(The phrasing “within 90% of its closest approach” is unclear, but an example on Nolle’s website shows that he means that the Earth-Moon distance is in the lowest tenth of its range.)
The term supermoon is not widely accepted or used within the astronomy or scientific community, who prefer the term perigee-syzygy. Perigee is the point at which the moon is closest in its orbit to the Earth, and syzygy is full or new moon, when the Earth, the moon and the sun are aligned. Hence, supermoon can be regarded as a combination of the two, although they do not perfectly coincide each time. 
The size and brightness of an object follows an inverse-square law, which means that a full moon at perigee is 12% larger and brighter than an average full moon. However, because the offset of the moon’s orbit versus its phases is only two days, this change in appearance is gradual from month to month and therefore is not usually noticeable to a casual observer.