The object was discovered in 1892, and in 1903 Max Wolf gave a very picturesque description of it: "a burning body from which several enormous curved flames seem to break out like gigantic prominences". That description is the origin of the name of the nebula being used today. Because of it's late discovery the nebula is not listed in the NGC catalogue, only in its first supplement called the Index Catalogue of Nebulae and Clusters of Stars published in 1895. The Flaming Star Nebula is identified as IC 405 in the Index Catalogue.
The nebula is located about 1500 light-years away from us. The physical phenomenon in it is the usual: hot young star ionises the hydrogen atoms in the cloud by its intensive UV radiation, then the atoms radiate the excess of energy by emitting photons. The cloud mostly consists of atomic hydrogen appearing red in the photo, but it also contains some dust rich in carbon which reflects the star's blue light, hence those regions appear bluish. But this nebula is also very different from the other HII regions.
While most of the hydrogen clouds are being ionised by young stars formed of the cloud itself, the case of IC 405 is different. The source of the ionisation is the star called AE Aurigae (the brightest star in the picture), which wasn't born here, it's only traversing through the area. Analysing the star's proper motion revealed that it might have formed near the Orion Nebula as a member of a binary system. Then, 2 million years ago, the binary system collided with another binary system resulting the stars being ejected in four different directions. Two of the other three stars was found too: 53 Arietis in the constellation of Aries, and µ Columbae located in the southern sky. These stars are moving away from each other at velocities over 100km/s, and their trajectory can be tracked back all the way to the Orion Nebula, where the collision happened. Stars which are moving away from their place of formation due to similar reasons are called runaway stars. So AE Aurigae is only traversing through and ionising the hydrogen cloud in Auriga.
AE Aurigae itself is anything but common. Its mass is 17 solar masses, has a diameter more than 6 times bigger than Sun's and is 33000 times more luminous than our Sun. Despite of its enormous size astronomers classify it as O-type main sequence dwarf, which is another one of misleading notations in astronomy. Red, orange and yellow dwarf stars are indeed smaller than other stars of the same colour, but in the case of hot blue and white stars designation dwarf/giant does not refer to size, because there is no significant difference between them, but it refers wether the star is on the main sequence or not. AE Aurigae is on the main sequence, hence it is designated as dwarf, however, based on its physical characteristics, it deserved better.