The first three realms are the human realm, the demi-god realm, and the god realm. The other three are the animal realm, the hungry ghost realm, and the hell realm. Although there are no souls or eternal selves to be reborn, we are changing states of being, and our actions constantly create new individuals that are considered to be “us”. For example, a 40-year-old is not the same person as he was at the age of 20, but he is the product of his past actions, and is still experiencing their consequences. By the same process, the people we are in the following lives are the result of this process governed by Karma.
Some believe that the realms should be understood as metaphors, rather than actual worlds into which one may be reincarnated. The realms then exist in our minds, and which realm we each belong to depends on our actions in this human world.