Surtr is already in position before anything exists, and he is still there when everything is finished. No other figure in Norse mythology is present at both ends.
Gylfaginning places him first: before the earth, before the gods, before Ymir, the region called Múspell lay to the south, bright and hot and burning, impassable to anyone not native to it — and Surtr sits at its border, holding a flaming sword, waiting. Snorri says that at the end of the world he will go forth, harry, defeat all the gods, and burn the whole world with fire.
He does not want anything. He does not oppose anyone. He waits, for the entire duration of the universe, and then he goes.
What the poems say
Völuspá has him come from the south with the destroyer of branches, his sword shining like the sun of the gods; the rocks crash, giantesses stumble, men tread the road to Hel, and heaven splits. Later: Surtr's fire — Surtalogi — plays against heaven itself.
Vafþrúðnismál asks who will survive when Surtr's flame is quenched, and the answer names Víðarr and Váli, and Móði and Magni with the hammer. After the fire, not despite it. The phrasing assumes the burning as a scheduled event with an aftermath, and the survivors are counted from the far side of it.
He kills Freyr, who gave away his sword for a marriage.
Fáfnismál names the island Óskópnir as the place where Surtr and the Æsir will meet, and says the bridge Bifröst will break under them.
Múspell, and the word's odd history
The name Múspell is not obviously Norse, and its cognates appear outside Scandinavia in a specifically Christian context.
The Old High German poem Muspilli, from the ninth century, describes the end of the world in Christian terms — the soul's fate, Elijah's blood falling on the earth, mountains burning, no stone standing — and uses muspilli for that conflagration. An Old Saxon form appears in the Heliand.
So a word for the fiery end of the world is attested in continental Germanic Christian poetry before it appears in Icelandic. That does not settle whether the concept is native or borrowed — the Christian poets may have used an inherited pagan word for a familiar idea, which is what missionary poets normally did — but it is one of the strongest single pieces of evidence in the long argument about how much of Ragnarök reflects Christian eschatology.
In Snorri, Múspell is a place, Múspellsheimr, and "Múspell's sons" are its inhabitants, who ride to the last battle and break the bridge with their weight. In the poems it is much less clearly a location. Snorri's fire-realm opposite an ice-realm is a tidy cosmological symmetry that the Eddic poems do not straightforwardly support.
Surtshellir
In western Iceland, in the lava field of Hallmundarhraun, there is a lava tube about a mile and three-quarters long. It is called Surtshellir — Surtr's cave — and the name is recorded in Landnámabók, so it was in use by the twelfth century at the latest.
The cave was formed by an eruption that has been dated to around the ninth century, within living memory of Iceland's settlement. Archaeological work published in recent years has found a substantial stone structure inside it, together with animal bones and imported objects, which the excavators interpret as evidence of ritual activity carried out in a cave that had recently been made by fire coming out of the ground.
That is the closest Norse mythology gets to a documented encounter with its own imagery. Settlers arrived in a country where the earth opened and burned, and they named the resulting hole after the being who is going to burn everything.
Whether Iceland's geology produced Surtr is a separate and unanswerable question — Norwegian and Danish settlers brought their beliefs with them from places with no volcanoes. But the naming shows how the material was used.
In 1963 a volcanic island rose out of the sea off Iceland's south coast and was named Surtsey. It is now a UNESCO World Heritage Site and a closed biological reserve, studied as a record of how life colonises new land.
Not a giant, exactly
Snorri does not call Surtr a jötunn. He is a being of Múspell, which is its own category, and the fire-people are never given a genealogy, a hall, a feud, or any of the social apparatus the giants have. The jötnar in Norse myth are relatives, in-laws and enemies of the gods; Múspell's sons have no relationship with anyone.
His name simply means "the black one" or "the swarthy one," from a root surviving in Icelandic svartur and English swart. A black figure with a burning sword is either a description of charred rock or of a shadow against fire, and the sources do not elaborate.
For the beings he is not related to, see the giants; for how his fire compares with other traditions' endings, Ragnarök and the other endings; and for the Norse overview.
Does Surtr die at Ragnarök?
No source says so, which makes him almost unique. The great confrontations at the end are mutual: Odin and the wolf, Thor and the serpent, Týr and the hound, Heimdall and Loki all destroy each other. Surtr kills Freyr and then sets everything alight, and the texts move on to the world rising again without accounting for him. Vafþrúðnismál's "when Surtr's fire is quenched" implies the fire ends; nothing implies he does.
Is Surtr's sword the same as Freyr's?
They are distinct weapons, and the confusion is understandable. Surtr's blade is described as shining brighter than the sun and is his from the beginning. Freyr's sword — the self-fighting one he handed to his servant as payment for a courtship — is simply gone from the narrative, and its absence at the end is what leaves him defenceless. A few modern retellings merge them so that Surtr kills Freyr with Freyr's own weapon, which is a good story and is not in any medieval source.