Buddhism
(*referenced from http://www.khandro.net/doctrine_trikaya.htm)
In Buddhism, the word trikaya refers to the three kayas, bodies, or levels of Buddhahood–the dharmakaya, samboghakaya, and nirmanakya. In English… truth-body, bliss- or enjoyment-body, and activity-body.
A simplified explanation is that the dharmakaya (truth-body) is the Absolute. It is the source of everything… not different from the Void.
The sound Aum (Om) evokes the Absolute. One explanation found in the Hindu Puranas is that it is the grunt of the Goddess as she gives birth to creation. In Buddhism, that which it represents is entirely unborn–pure creative potential.
The 3 components of this syllable, here in a Tibetan form, can also be understood as the kayas.
The samboghakaya (enjoyment body) is rarely experienced. Its description is likened to stories told of deities, and it has been referred to as “timeless communication.” The sound Ah, the expression of joyous wonder, is written and used to evoke it.
The nirmanakaya (activity body) is the phenomenal world–our reality. The sound Hum, which actually means us in Sanskrit represents it. It is the here-and-now, with all its future potential.
It may be helpful to think of the three as: abstract, mythic and human realms; or as the blank canvas, the paint, and the hands that do the painting.
Brahmanism - the Vedas & Upanishads
(*referenced from http://www.cosmiclight.com/ofquasarsandquanta/omnipresence.htm)
Brahmanism is the forerunner of both Hinduism and Buddhism and provides us with the oldest texts (the Vedas) and best preserved metaphysical system of teaching on our planet. Brahman is the term used to refer to transcendental omnipresence, and it is attributed with the characteristics of consciousness and love -- it is a non-manifest yet living state of being -- pure spirit. This is expressed in the Sanskrit word Saccidananda, which is a run-together of three words, Sat, Chit, and Ananda, meaning, Existence, Consciousness of Existence, and Love of Existence, or simply, Being-Consciousness-Bliss. This is the trikaya, the three-bodied or triple-aspect characteristic of Brahman. The Hindu trinity of Brahma, Vishnu, and Shiva (the Creator, the Preserver, and the Transformer) are personifications of the trikaya. Krishna, Indra, and all other gods and enlightened teachers of the tradition, historical and mythological, are manifestations of Vishnu. (Note the difference between the words Brahma and Brahman, the former being a masculine noun, the latter being neutral.)
As pure metaphysical principles, the trinity is the same in any tradition. The first body of the trikaya is fully transcendental, like the Universal Singularity "just before" the Big Bang. The second body of the trikaya is the shining-forth, the Dharmakaya, the perfect embodiment of Divine Law, and is known variably as Prana, Life Force, Cosmic Light, Supermind, Universal Consciousness, Buddha-Consciousness, Christ-Consciousness, the Word, Logos. The third body of the trikaya is Brahman manifest as the Universe, the Divine Play, leela, the cyclic movement of the Cosmic Dance itself.