Those realms whose denizens are more subtle, longer-lived and enjoy greater pleasure than us humans are collectively referred to as Heaven. Rebirth in heaven is the result of performing meritorious actions, as for instance acts of generosity or kindness, while on Earth. There are numerous levels and stations within levels in these realms.
Broadly speaking, the Realms of Heaven may be divided into three levels. There are the Sensual Heavens, the Fine-Material Heavens and the Immaterial Heavens.
The Sensual Heavens are part of the kama-loka, the Plane of Sensuality which includes the human realm and the lower realms as well. The gods of the sensual heavens, known as devas, enjoy refined versions of the sense pleasures known to humans; food, sex, music, dancing and so forth. These gods live very long life spans, but they are not immortal. Also included in the sense-desire sphere are lesser deities that dwell bound to this earth, in big trees and other wild places.
The sensual heavens are six in number, in ascending order they are;
Beyond this realm we cross a threshold and come to a level beyond even the most refined sensuality. This is the realm of the Brahma gods; also called the fine-material realm. Beings here have fantastically long life-spans. They have no gender and take no material food. They are said to be self-luminous and to feed on bliss.
Even higher are the immaterial realms whose denizens are pure mind without any corporeal form whatsoever. Such beings cannot be said to occupy any definite location in space and exist as pure idea.
One interesting aspect of this Buddhist cosmology of the heavens is the gradual evolution towards more subtle and refined states of bliss. The lower levels of heaven enjoy quite worldly pleasures of music, dance, sexuality and feasting. These aspects become gradually refined as we move upward and are transcended altogether in the Brahma Realms which enjoy states of consciousness equivalent to the jhanas, or meditative absorptions. Their bliss is completely non-sensory in nature.
The other aspect to be noted is that no being in any of these realms is immortal. Even the Brahma Gods pass away after long ages and are reborn elsewhere. However, some of these beings are so long-lived that they falsely imagine themselves to be immortal.
"Dawn of the Dhamma" by Ajahn Sucitto, pub. Buddhadhamma Foundation, has some fascinating material on the heavenly realms.
Within the scriptures;
Majjhima 37 has an interesting description of the Heaven of the Thirty-Three.
Digha 49 tells the story of the Buddha's encounter with a Brahma God who was under the delusion that he was immortal.
Digha 18 has a story which involves several classes of gods and sheds some light on their nature.
Digha 20 contains a long verse section enumerating the various gods.