A nova was an event in which a star dramatically increased in brightness for a relatively short period of time.
A supernova could be induced by firing an antimatter missile into a nova's core. (DIS: "Such Sweet Sorrow") After finding an entire solar system reduced to rubble and asteroids, James T. Kirk stated that only a nova could do such a thing. (TOS: "The Doomsday Machine")
The Fabrina solar system went nova some ten thousand years before the Earth year 2268, resulting in the destruction of its planets. Towards the end, the Fabrini people lived underground to protect themselves. (TOS: "For the World is Hollow and I Have Touched the Sky")
Kataan's sun went nova in the 14th century, destroying all life on the planet. The star's brightening was noted by the natives of the planet, who launched a probe to preserve some of their culture. (TNG: "The Inner Light")