Surtur was native to the extra-dimensional plane of Muspelheim and was the mortal enemy of the Asgardian ruler Odin and his son Thor. Surtur and the ice demon Ymir were older, and therefore more powerful immortals than Odin and Thor, who were always hard pressed to defeat them. Surtur was imprisoned for a long time within the depths of the Earth, but was once freed by Loki and set aganst the Earth when Odin visited there to break the romance between Thor and Jane Foster. Thor used Odin's magic sword to send Surtur to outer space, where he was bound against a magnetic asteroid. He was next summoned to Earth together with Ymir when the Spell of Fire and Ice was cast by the Sons of Satannish.
Surtur's role in the Ragnarok Cycle began by forging/reforging Twilight — a huge magical blade — and then sending his legions of fire demons to Earth, to draw Asgard's armies away from their capital city. Surtur then crossed Bifrost, the Rainbow Bridge, and attempted to destroy the city once and for all. Odin, Thor and his adopted brother Loki, however, made a last stand and eventually defeated Surtur - at the cost of Odin, who fell with his foe into a dimensional rift. After the final Ragnarok, Beta Ray Bill briefly visited the ruins of Asgard, and saw Surtur's massive form falling from the sky. Surtur was still clutching Twilight, although the sword was broken during Bill's battle with the demon Asteroth.
The Final Ragnarok
Surtur apparently died once and for all during the final Ragnarok when Thor managed to break the cycle. He was trapped in an afterlife dimension fighting a continuous battle with Odin, who prevented Surtur from escaping and returning to Earth by sacrificing himself over and over.
When the Serpent was released by Skadi, the reborn Loki tried to find a way to stop him from destroying everything. He went to Limbo and made a deal with Surtur, promising to release him in Asgard in exchange for his Twilight's Shadow. Loki used the Shadow to rewrite the Serpent's history, giving him a weakness. He then released Surtur in the Serpent's Dark Asgard, tricking him. After destroying Dark Asgard, Surtur returned home to Muspelheim.
Surtur made a deal with Master Wilson of Otherworld, helping to create his Manchester Gods to modernize Otherworld. Wilson was entirely unaware of Surtur's true nature and intentions. He used the Manchester Gods in a plot to destroy all of reality. Wilson destroyed the Manchester Gods at Loki's urging, but Surtur still was strong enough to destroy Asgardia and the World Tree. Thor killed him and his power was sent into Asgard-Space by Odin.
Surtur was depicted as an immense and malevolent being whose possesses the power of a thousand blazing suns. Surtur is an enormous fire demon, standing over 1,000 ft. in height. He is more of a force of nature than a physical foe. He possesses superhuman strength, stamina, and durability far surpassing that of Thor. He is possibly a being composed of "living" flame so strong that he can affect the Earth's temperature from Asgard and can manipulate cosmic energy to generate intense heat, flames or concussive force. He can also manipulate cosmic energy for various effects, including levitation, molecular manipulation of himself, inter-dimensional teleportation, and immortality. He is vulnerable to intense cold, and can be imprisoned by certain magical spells or by other beings wielding cosmic energy powers equaling his own; Surtur's powers are usually shown to equal those of Odin. Surtur is a master warrior and swordsman, and has a prehensile tail. He possesses vast knowledge of ancient and arcane wisdom.
The Eternal Flame has an unknown connection to Surtur. When in its vicinity, Surtur claimed it increased his powers. It is unknown to what extent this power increase leads to.
Twilight: Surtur possesses the giant sword Twilight, also known as the Sword of Doom, composed of an unknown metal. The sword is magic, capable of manipulating vast amounts of mystical energy, such as shattering dimensional barriers and inhibiting Odin's powers. Loki has temporarily tapped into the power of the sword to change Thor into a frog (Thor is normally resistant to this type of magical transformation) and making the Asgardian populace sick (Asgardians are normally immune to disease). Morgan Le Fay tapped into the power of the sword to reshape the entire planet Earth from modern day into a medieval world after using the chaos magic of the Scarlet Witch to "bridge the gap" between her personal faerie powers and the Asgardian magics bound to the blade. When the sword is bonded with the Eternal Flame, its powers are further increased to an unknown level.