The Nine Realms are nine individual worlds that, while located in separate star systems, are systematically connected by the branches of Yggdrasil. The inhabitants of the realms are mostly associated with each other rather than the other advanced species residing beyond the realms. Earth, where humanity resides, is one of the Nine Realms, but its inhabitants are considered to be too underdeveloped by the other races to associate with.
Asgard is considered to be the head of the Nine Realms, and its inhabitants, the Asgardians, are arguably the most powerful species in the realms. Odin, the former ruler of Asgard, and his troops act as the protectors of the Nine Realms and even other regions of space. They act as a police force that tries to preserve peace. The Asgardians produced a sister race which settled on the planet Vanaheim, and are referred to as the Vanir. Nidavellir, home of the Dwarves, neighbors Asgard, and a strong relationship is present between the two. The world of Alfheim also lies close to Asgard.
Slightly below Asgard is Jotunheim, which is inhabited by the Jotuns, also known as the Frost Giants. The Frost Giants have tried to conquer the other realms a number of times, but were thwarted in each attempt by the Asgardians. Located above Asgard is Muspelheim, a world that is bathed entirely in flames and is home to many beasts that manifested from the fires. Located at the bottom of Yggdrasil are Svartalfheim and Niflheim. The former was once home to the Dark Elves before a cataclysmic battle against the Asgardians ravaged the planet's surface and nearly drove the species extinct. The latter is a world notable for being the location of Hel, a shadowy area that the Asgardians believe holds the souls of those in the Nine Realms who have died.
Portals opening to the Realms during the Convergence. Every five-thousand years, an event called the Convergence would take place in Yggdrasil where the spatial boundaries between the Nine Realms gradually decrease until becoming almost non-existent. This would result in the formation of portals between the worlds.
Heimdall of Asgard watches over the Nine Realms and other regions of space. He mentions to Thor that from his post at his observatory he can see nine realms and ten trillion souls. This is the approximate number of inhabitants throughout in the Nine Realms or in the region of space the Asgardians preside over.
The Asgardians preside and watch over not only the Nine Realms, but other planets too. Therefore, many species of the Nine Realms have had history of contact with species and civilizations from beyond the Nine Realms.
The Nine Realms:
Asgard
Midgard
Jotunheim
Svaralfheim
Vanaheim
Nidavellir
Niflheim
Muspelheim
Alfheim