The trikaya or 'three bodies' teaching in Mahayana Buddhism describes the three bodies of a Buddha, which also correspond in Tibetan Buddhism to the three vajras of body, speech, and mind. Because Mahayana Buddhism teaches that anyone may attain Buddhahood, these kayas are relevant to everyone, and in fact, in some traditions, such as the Dzogchen teachings within the Nyingma school of Tibetan Buddhism, practices have evolved for realizing all three.
The three kayas are the dharmakaya (truth body), sambhogakaya (bliss body or 'body of mutual enjoyment'), and the nirmanakaya (body in time and space.) The nirmanakaya is most closely related to what we normally think of as our physical body the form that we take as a human being - although because some Mahayana traditions posit other planes of existence, there are other forms of nirmankayas described in some teachings. Also, our physical body is not the only aspect of our nirmanakya it includes our subtle, or energy body, encompassing the chakras, as well as our emotional body and other emanations, depending on the tradition.
The sambhogakaya, usually translated as either 'bliss body' or 'body of mutual enjoyment' is an emanation for teaching the dharma and aiding other beings on the pathway to enlightenment. 'Enjoyment' in this case, doesn't refer to worldly pleasures, but to the enjoyment of teaching the dharma and helping other beings to awaken. An enlightened being may manifest a sambhogakaya wihout manifesting a nirmanakaya, as is the case with some 'yidams', or meditative deities, in Tibetan Buddhism. Other traditions such as Pure Land Buddhism, describe the sambhogakaya as a 'reward' body that is realized when a bodhisattva completes his vows and becomes a Buddha Amitahba, Vajrasattva and Manjushri are considered examples of these.
The dharmakaya is pure, primordial awareness or light itself. It is the embodiment of truth or dharma, and does not itself have form, but is the root of all perceptions of form and sense. 'Dharma' in this sense does not mean the teachings of Buddhism, as it sometimes does, but instead means the undifferentiated source of these teachings and all reality what the teachings point to, or what is directly realized as the fruit of practice. An enlightened being comes to embody dharma through the dharmakaya.
When we are talking about the kayas in relation to the Buddha, the nirmanakaya was the historical Buddha the man born as a prince around 500 B.C., who left home to realize enlightenment, and from whom we have many teachings. The sambhogakaya is the level of Buddha that we can still connect with, as a teacher, and even doorway, to the teachings when we use Buddha a meditative focus. The dharmakaya is enlightenment itself, as embodied by the Buddha.
In the Dzogchen teachings of the Nyingma school of Tibetan Buddhism, these three kayas are also related to the vajras the dharmakaya to the vajra of mind, the sambhogakaya to the vajra of speech, and nirmanakaya to the vajra of body. In some teachings these are also taught to correspond to specific chakras, or energy centers the crown for the nirmanakaya, the throat for the sambhogakaya, and the heart for the dharmakaya. Meditation practices related to these chakras help a practitioner realize and integrate these bodies.
Yet another body is taught in this tradition as well the rainbow body (the image above is of Padmasambhava, the historical founder of Tibetan Buddhism, in rainbow body form.) This body is a body of light manifested when the dharmakaya, sambhogakaya, and nirmanakaya are all in accord with each other. It represents realization beyond the dualisms of mind and body, or mind and matter. At death, a Buddha who has manifested the rainbow body is said to leave only fingernails or hair behind the rest of the nirmankaya is transmuted into light.