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.
1. Deva-gati, the Realm of Devas (Gods) and Heavenly Beings
In Buddhist tradition, the Deva realm is populated by godlike beings who enjoy great power, wealth and long life. They live in splendor and happiness. Yet even the Devas grow old and die. Further, their privilege and exalted status blind them to the suffering of others, so in spite of their long lives they have neither wisdom nor compassion. The privileged Devas will be reborn in another of the Six Realms.
2. Asura-gati, the Realm of Asura (Titans)
The Asura are strong and powerful beings who are sometimes depicted as enemies of the Deva. Asura are marked by their fierce envy. The karma of hate and jealousy causes rebirth in the Asura Realm.
Zhiyi (538-597), a patriarch of the Tiantai school, described the Asura this way: "Always desiring to be superior to others, having no patience for inferiors and belittling strangers; like a hawk, flying high above and looking down on others, and yet outwardly displaying justice, worship, wisdom, and faith -- this is raising up the lowest order of good and walking the way of the Asuras." You may have known an Asura or two.
3. Preta-gati, the Realm of Hungry Ghosts
Hungry ghosts (preta) are pictured as beings with huge, empty stomachs, but they have pinhole mouths, and their necks are so thin they cannot swallow. A hungry ghost is one who is always looking outside himself for the new thing that will satisfy the craving within. Hungry ghosts are characterized by insatiable hunger and craving. They are also associated with addiction, obsession and compulsion.