Astronomical definition
From time to time, a very bright star will appear in the heavens, shine brilliantly for a time, then disappear. One such historical event, the Star of Bethlehem, could have been a nova.
Many stars have a companion star, forming a binary system, each orbiting the other. Most double stars have one companion significantly larger than the other, which may be large enough to form a red giant, which then collapses to form a white dwarf. When this happens, it may draw matter from the less dense companion to form an accretion disk around itself (rather like a much larger version of Saturn's rings). The build-up of pressure and temperature caused by this layer may become high enough to start fusion, at which point an explosion is triggered, which blows the material off into space as an expanding shell of energetic gas. (If the star does not lose too much of its mass, or continues to leech material from its companion, it may repeat after a period, which may be as short as fifty years. Many optically variable stars are periodic novae.)
This explosion can be incredibly bright, as much as 50,000 times brighter than our own Sun, and consequently, is visible over vast astronomical distances. What appears to the naked eye is a new star (stella nova) which may outshine all others for a few days or weeks, before vanishing again. The remnants of this expanding sphere of gas may be seen through telescopes as a small bright ring, for a long time afterward. Although not as spectacular as nebulae produced by supernovae, these are nonetheless beautiful objects.
So, apart from their sudden beauty, why the interest in novae? Well, for one thing, elements heavier than iron cannot be produced by fusion in 'normal' stars - our own Sun is unlikely to produce anything heavier than carbon. The more energetic novae may produce some transferric elements, although supernovae are the most prolific creators of the heavier atoms. We owe our very existence to these violent and beautiful objects.
Thanks to unperson who pointed out that the explosion happens in the star, not the accretion disk.