Everything the Buddhas and Bodhisattvas
do and not do are expressions
of perfect compassion for all.
The Buddhas are described as having three bodies (Trikāya 三身) or aspects of existence, though they are in ultimate reality one in all and all in one. They are as follows.
 The Truth Body of Buddhas: The truth body of a Buddha (Dharmakāya 法身 ) is the embodiment of the Dharma (truth itself) that is eternally present everywhere, expressed in the natural laws of the universe and the workings of these laws. Sometimes we catch a glimpse of this wonderful reality when we are at peace and at one with everything. This body of truth is in all things though it is beyond shape and form. It is represented by (Mahā)vairocana Buddha (毘盧遮那佛), the central and universal Buddha who is preaching the truth right here and now. He is both one and many at the same time as he manifests in many forms. Our inability to see or hear him is due to our defilements.
The Buddha taught, ‘He who sees the Dharma (the truth) sees the Buddha. He who sees the Buddha sees the Dharma.’ A Buddha, having realised the truth, becomes equal to the truth. Though there are many Buddhas, all Buddhas are one and the same, being no different from one another in the Dharmakāya, which is the oneness of truth.
The Dharmakāya exists simultaneously with the Saṃbhogakāya and Nirmāṇakāyas (as below). With the moon representing the Buddha, the Dharmakāya is like the rays of the moon that shine at night. These rays of light might not be visible to the eye as they do not illuminate the darkness of space, but they pervade it fully everywhere.
 The Bliss Body of Buddhas: The bliss body of a Buddha (Saṃbhogakāya 报身) or Rocana Buddha (卢舍那佛) is the magnificent blissful reward body of a Buddha in his Pure Land, which is his reward land (报土), where he can be seen. It is the aspect through which each Buddha rejoices in the truth, in teaching the truth, and in leading others to the realisation of the truth. Because each Buddha has practised through countless ages to attain perfect compassion and wisdom, each has immeasurable peace, merits and happiness, as expressed in the Saṃbhogakāya. Buddhas usually do not appear in this form among humans as we lack the merits to perceive them this way. Instead, they manifest as Nirmāṇakāyas (as below).
With the moon representing the Buddha, the Saṃbhogakāya is like the unclouded full moon shining bright in its total splendour.
 The Manifestation Body of Buddhas: An example of a manifestation body of a Buddha (Nirmāṇakāya 应化身) in our world is the transformed body of the historical Śākyamuni Buddha (释迦牟尼佛). It is the Buddha expressed in a human form. A Buddha can also manifest in many different forms at the same time to teach the truth to many beings. Having attained perfection, the abilities of a Buddha are far beyond that of ordinary humans. It is out of compassion, to be an example, and to teach the truth to many, that a Buddha chooses to appear in this form that we can relate to. When the Buddha entered Parinirvāṇa, only his physical body passed away. The essence of his enlightenment still exists in the form of the Dharmakāya, Saṃbhogakāya and other Nirmāṇakāyas. Today, the physical relics of the Buddha’s manifested body are enshrined in stupas all over the world.
With the moon representing the Buddha, the Nirmāṇakāya is like a reflection of the moon upon a lake. One moon can be reflected differently in many lakes at the same time.
Be A Lamp Upon Yourself (6th Edition)
Edited (and here expanded) by Shen Shi’an