The Six Realms are a description of conditioned existence, or samsara, into which beings are reborn. Although sometimes they are described as "real" places, more often these days they are appreciated as allegories.
The nature of one's existence is determined by karma. Some realms seem more pleasant than others -- heaven sounds preferable to hell -- but all are dukkha, meaning they are temporary and imperfect. The Six Realms often are illustrated by the Bhava Chakra, or Wheel of Life.
(These Six Realms are the realms of the world of desire, called Kamadhatu. In ancient Buddhist cosmology, there are Three Worlds containing a total of thirty-one realms. There are Arupyadhatu, the formless world; Rupadhatu, the world of form; and Kamadhatu, the world of desire. Whether it's useful to know anything about the thirty-one realms is a matter to debate, but you might run into them in old texts.)
Please note that in some schools the realms of Devas and Asuras are combined, leaving five realms instead of six.
In Buddhist iconography, a bodhisattva is placed in each realm to help beings out of it. This may be Avalokiteshvara, bodhisattva of compassion. Or it may be Ksitigarbha, who travels to all the realms but who has made a special vow to save those in the hell realm.
Deva-gati, the Realm of Devas (Gods) and Heavenly Beings
Asura-gati, the Realm of Asura (Titans)
Preta-gati, the Realm of Hungry Ghosts
Tiryagyoni-gati, the Animal Realm
Manusya-gati, the Human Realm
