In Norse mythology, Surtr is some sort of being of fire, generally interpreted to be a giant, on account of his main narrative role being to side with the frost giants against the Æsir gods during the cataclysmic battle known as the Ragnarök, in which the two groups of enemies work to almost annihilate each other, destroying the world in the process.
Surtr is the main agent of this disintegration, having emerged from Múspellsheimr, the region of perpetually burning flame forming the extreme southern end of the universe.
It is a world too luminous and glowing to be entered by those who are not indigenous there. He who sitteth on its borders to guard it is named Surtr. In his hand he beareth a flaming falchion, and at the end of the world shall issue forth to combat, and shall vanquish all the gods, and consume the universe with fire.
My gloss of I.A. Blackwell's 1907 translation of the Gylfaginning [from §4]
Among those lending their muscle to the side of the giants on this fateful day, Snorri Sturluson mentions, in the Gylfaginning, Surtr leading a group that he calls the Sons of Múspell, who likewise tend to be interpreted as fire-giants, or some variety of fire-daemon. With this horde in tow, "Surtr shall ride first," brandishing "a splendid sword, from which radiance shines brighter than from the sun" with flames bursting forth "both in front of and behind him". (The 19th-century German artist Friedrich Wilhelm Engelhard apparently thought that what Surtr rides is a horse.)
To get to the battlefield upon which they will contend with the Æsir, Surtr and his band go via Bifröst, the rainbow, which is also a bridge that the deities have used throughout history to travel between heaven and earth. Either from the intensity of Surt's fire or from the weight of his troops, Bifröst collapses, marking a point commencing the demolition of the universe's infrastructure.
Aside from reducing the rest of the cosmos to ashes and rubble, Surtr also engages in a duel against the god Freyr, whom he defeats, since Freyr does not have the good sword he long ago gifted to his servant Skirnir. According to the 1993 translation of Rudolf Simek's Dictionary of Northern Mythology (p. 303), Freyr and Surtr kill each other in this conflict. I, however, don't see Surtr's death mentioned explicitly in any of the primary sources.
The poem Vafþrúðnismál, which Snorri quotes in the Gylfaginning, describes some of the Æsir as emerging unscathed from the carnage after "Surtr's Fire has been slaked". This, to me, is ambiguous: Are we to understand that Surtr and his forces have burned themselves out, consumed by their own flames; or did they rather simply keep pouring on the heat until they were satisfied with their efforts at unmaking the world? And then maybe they headed back home to Múspellsheimr?
It is also unclear to me whether we are to understand the original realms at the northern and southern poles of the universe to have remained eternally unchanged, with perpetual heat and flame in the south; and misty, frosty chill and darkness rolling on endlessly in the north. As far as I'm aware, the origins of Surtr and the Sons of Múspell are never elaborated upon in the sources that we have (presumably they are the indigenes of the fire-world mentioned in Gylfaginning 4 [see above], who are able to withstand its blazing heat).
But might there be any insight in the old texts, or in scholarship pertaining to them, on whether we should expect these fire-folk to live through the conflagration which ends the world? (In doomsday's aftermath, we do see certain features of the universe—which one might think susceptible to incineration, such as the cosmic tree Yggdrasil, as well as a couple of humans—somehow surviving Surtr's Fire.)
