As we sit here on Midgard, Midgard sits on Yggdrasil, the world tree. Yggdrasil is, put simply, the universe. On this tree, like ripe fruit, hang the nine worlds.
Alfheim - Alfheim is the home of the Alfs (Elves). Beings of light, it is also the home of Frey, who rules over them.
Asgard - Asgard is the home of the Aesir. It is the place where the many halls meet, and the place of Valhalla, the most famous of the Aesir's halls.
Hel - The land of the dead. Also the hom of Hel (daughter of Loki).
Jotunheim - Jotunheim is the the home of the Jotun. As they are the enemy of the Aesir, little is known of this place.
Midgard - Midgard is our home. Earth.
Muspelheim - Muspelheim is a land of fire. A place forever ablaze, it is the opposite of Niflheim, and the home of Surt and the fire-giants.
Niflheim - Niflheim is a land of ice.
Svartalfheim - Svartalfheim is the home of the Dark Elves (also known as Dwarves).
- Vanaheim is the home of the Vanir. Mind you, since they've
pretty much moved into Asgard, it must be a lonely place.
Yggdrasil has several inhabitants. There is the squirrel Ratatosk, who scurries around telling lies. There is the serpent Nidhug, who gnaws at its roots. There are deer, hawks, and other creatures.