Asgard:

Originally, it is thought, Asgard was a part of the world of humans but Snorri places it in the heavens, connected to Midgard by Bifrost, the rainbow bridge. Asgard is the home of the Aesir, the majority of the Norse pantheon who warred with other gods known as the Vanir, made peace, and exchanged hostages to maintain that peace. Therefore, even though Asgard is primarily the home of the Aesir, there are Vanir who live there just as there are Aesir in Vanaheim.

The best-known gods of the Norse pantheon are Aesir or live in Asgard: Odin, Thor, Loki, and Baldr. Asgard is depicted as a celestial city of high towers surrounded by a great wall. Odin's famous hall of Valhalla, where his throne may have been located, is in Asgard. However, a place-name or object, Hildskjalf, is mentioned from which Odin can gaze out over the entire world and it is unclear whether this is his royal hall (separate from Valhalla) or his throne.

Alfheim:

Alfheim also exists in the heavens, not far from Asgard, and was the home of the light (or bright) elves and, after Snorri, all the elves. It was presided over by the Vanir god Freyr who was one of the hostages sent from Vanaheim to Asgard at the conclusion of the war. The elves are magical beings, bright and beautiful, who inspired the arts, music, and creativity in general.

Helheim:

Hel (sometimes known as Helheim) is a dark, gloomy realm presided over by Hel, daughter of Loki, and sister of the Midgard serpent and Fenrir the wolf. When Loki's children were born, Odin knew they would cause trouble and so sought to place each one where it would do the least harm. He placed the Midgard serpent in the seas which surround the world, had Fenrir chained up, and threw Hel into a dark realm beneath the roots of Yggdrasil. This realm was then surrounded by a wall with only one gate and could only be reached by traveling downhill on a long, long path (known as Helveg – the way or road to Hel) and crossing a dangerous river of weapons.

Jotunheim:

Jotunheim (sometimes referred to as Utgard) is the realm of the giants and Frost Giants and is located near both Asgard and Midgard. Jotunheim/Utgard was considered beyond the realm of order, a primordial place of chaos, magic, and untamed wilderness. Loki, the trickster god of mischief, came from Jotunheim but lived in Asgard. Jotunheim was considered best avoided but there are a number of tales involving gods of Asgard purposefully traveling there.

It was separated from Asgard by the river Iving, which never froze and was difficult to cross, but Odin traveled to Jotunheim to Mimir's well of wisdom and Thor also went there to the stronghold of the giant Utgarda-Loki. Anything could happen to a person in Jotunheim as the tale of Thor and Utgarda-Loki makes clear: nothing Thor experiences on his journey is what it appears to be and, at the end of the story, the stronghold and everyone in it disappears.

Midgard:

The realm of human beings was first populated by Ask and Embla, from whom all other people are descended. After Odin, Veli, and Ve kill Ymir and create the world, they are walking along by the sea and find two trees, an Ash and an Elm. They create the first man from the Ash tree and the woman from the Elm. They understand, however, that these creatures are helpless and easy prey for the giants and so create Midgard to protect them. After humans are created, the gods create Asgard with its high walls for protection and are then assumed to have made the animals in Midgard and the rainbow bridge.

Muspelheim:

Muspelheim is the primordial realm of fire, according to Snorri, which was instrumental in the creation of the world. The Fire-Giant Surtr lives in this realm and will emerge at Ragnarok, the twilight of the gods, to destroy Asgard and everything else.

Nidavellir/Svartalfheim:

The realm of Nidavellier/Svartalfheim was below Midgard, deep in the earth, and the home of the dwarves who toiled there at their forges. It is a dark, smoky, place lit only by the fires from the forge and the torches on the walls. The gods seem to have decreed the realm of the dwarves based on their origin as given by Snorri. The dwarves were associated with craftsmanship and magic. They created Thor's hammer Mjolnir and Odin's spear and well as the god Frey's magic ship which can be folded up and carried in his pocket. They are also responsible for the Mead of Poetry which Odin steals from the giants and gives to the gods who then inspire poets, through drink, to create their verse.

Niflheim:

Niflheim, along with Muspelheim, is the oldest of the nine realms, the primordial land of ice, mist, and snow, from whence all life began. Niflheim, however, has nothing to do with the realm of the dead per se. It is a cold and misty realm where no one lives, not even the Frost Giants. Odin is said to have thrown Hel into Niflheim and to have then given her power over the dead and the lives of those in the Nine Realms but it is thought that she would have passed through Niflheim and into Niflhel (which just means “dark realm of Hel”) where she then ruled. 

Vanaheim:

Vanaheim is the home of the Vanir, the other family of Norse gods, who were associated with fertility and magic. The Aesir went to war with the Vanir but precisely why is unclear. It may be the war was fought over various practices of the Vanir which the Aesir considered unacceptable such as allowing incest and practicing a kind of magic the Aesir thought dishonorable. Whatever the war was about, it was concluded by a peace treaty in which hostages were exchanged and the Vanir sea god Njord and his two children Freyr and Frejya went to live in Asgard.