Dormammu is a demon that exists in a realm called the Dark Dimension.
Marvel Animated Universe
Dormammu and his army of Mindless Ones attempted to break through the barrier between Earth and the Dark Dimension. He caught Doctor Strange, but lost in a battle between him and Doctor Strange, A-Bomb and Hulk. He instead hid in Doctor Strange's amulet and escaped in to the real world but was defeated by the Agents of S.M.A.S.H., the house and Doctor Strange. Dormammu is considered to be one of Dr. Strange's toughest enemies. On Halloween, the Agents of S.M.A.S.H. encounter Nick Fury's Howling Commandos (consisting of Blade, Frankenstein's Monster, Man-Thing, N'Kantu, the Living Mummy, and Werewolf by Night) where they have been sent by Fury to apprehend the Agents of S.M.A.S.H. However, the Howling Commandos have a change of plans when they end up helping the Agents of S.M.A.S.H. prevent Dormammu from breaking into Earth's dimension and turning all of humanity into Mindless Ones.
Dormammu placed a spell upon the superhero Cloak to take control of him. With Cloak at his command, he used his teleportation powers to capture various mystics to be placed under his control. After kidnapping White Tiger and Iron Fist, he had Cloak capture Doctor Strange and confiscated a crystal called the Siege Perilous from Strange to open a portal strong enough to enable his army passage to Earth, and subsequently had them all placed under his control. However, his plan is hampered when Spider-Man and Cloak's partner Dagger free Cloak from the spell and eventually White Tiger and Iron Fist.
Unfazed by this turn of events and with the Siege Perilous fully charged, Dormammu has Doctor Strange aid him against extinguishing the heroes which proves fruitless for the heroes due to Dormammu's nigh invulnerability in the Dark Dimension. However, Cloak and Dagger manage to break the control over Doctor Strange who is able to injure Dormammu as the group escapes with the Siege Perilous in hand. When the group tries to escape through Cloak, Dormammu halts Cloak and uses him to enter Earth. But just as he arrives, Dormammu is rendered vulnerable and is banished back to the Dark Dimension by the combined powers of Spider-Man and Doctor Strange.
Due to the effects that the Infinity Gems are having on reality, Dormammu and the Mindless Ones emerge from a portal to the Dark Dimension causing the Avengers and Doctor Strange to fight them. Dormammu and the Mindless Ones are repelled by Black Widow using the powers of four Infinity Stones, namely Time Stone, Space Stone, Mind Stone and Reality Stone.
Dormammu appears as the primordial ruler presiding over the Dark Dimension. Desiring to conquer the universe, Dormammu seduces Kaecilius with promises of immortality, causing the Zealot to turn on the other Masters of the Mystic Arts. Kaecilius then began to make the preparations to bring his new master to Earth.
After bringing destruction to the Sanctums that kept the dark forces at bay, Dormammu begins to absorb Earth into the Dark Dimension. However, as he does this, Doctor Strange slips into his realm and confronts him, offering a bargain. Dormammu, angered by this intrusion, promptly kills Strange. However, using the Time Stone in the Eye of Agomotto, Strange creates an infinite loop where Dormammu would be forced to kill Strange again and again for eternity, with the entity unable to do anything else.
As the cycle repeats itself multiple times, Dormammu becomes desperate to escape it, and begs Strange to set him free. Strange agrees, on the condition that Dormammu leaves the Earth and takes Kaecilius and his Zealots with him. Dormammu accepts this and keeps his word, and seals the connection between the two dimensions.