This philosophical truth of simultaneous oneness and difference was propounded by Lord Śrī Caitanya Mahāprabhu, and it is known as acintya-bhedābheda-tattva. Brahmā, Nārada and all others are simultaneously one with the Lord and different from the Supreme Lord. We are all one with Him, just as the gold ornaments are one in quality with the stock gold, but the individual gold ornament is never equal in quantity with the stock gold. The stock gold is never exhausted even if there are innumerable ornaments emanating from the stock because the stock is pūrṇam, complete; even if pūrṇam is deducted from the pūrṇam, still the supreme pūrṇam remains the same pūrṇam. This fact is inconceivable to our present imperfect senses. Lord Caitanya therefore defined His theory of philosophy as acintya (inconceivable), and as confirmed in the Bhagavad-gītā as well as in the Bhāgavatam, Lord Caitanya's theory of acintya-bhedābheda-tattva is the perfect philosophy of the Absolute Truth.
(Srimad Bhagavatam----2:6:13-16----purport).

According to the Gauḍīya acintya-bhedābheda-tattva philosophy, anything which satisfies the senses of the Supreme Lord, Śrī Kṛṣṇa, is also Śrī Kṛṣṇa. For example, Śrī Vṛndāvana-dhāma is nondifferent from Śrī Kṛṣṇa (tad-dhāma vṛndāvanam) because at Vṛndāvana the Lord enjoys the transcendental bliss of His internal potency. Similarly, the house of the Pāṇḍavas was also the source of transcendental bliss for the Lord.
(Srimad Bhagavatam----3:1:2----purport).

As stated in Bhagavad-gītā (13.15), nirguṇaṁ guṇa-bhoktṛ ca: although the Lord is not attached to the external energy, He is nonetheless the master of it. The philosophy of Lord Caitanya, upholding that the Lord is simultaneously one with and different from His creation (acintya-bhedābheda-tattva), is very easily understandable in this connection. The planet earth explains that although the Lord is attached to the external energy, He is nirdhuta; He is completely free from the activities of the external energy. The Lord is always situated in His internal energy.
(Srimad Bhagavatam----4:17:29----purport).

The sunshine is light, the sun globe itself is light, and the sun-god is also light. However, the sunshine is not identical with the sun-god, Vivasvān. This is the meaning of simultaneously one and different (acintya-bhedābheda-tattva). All the planets rest on the sunshine, and because of the heat of the sun, they all revolve in their orbits. On each and every planet, the trees and plants grow and change colors due to the sunshine. Being the rays of the sun, the sunshine is nondifferent from the sun.
(Srimad Bhagavatam----4:31:16----purport).

As fire appears separate from wood and as the air flowing through the nostrils and mouth of the body appear separate from the body, so the Paramātmā, the Supreme Personality of Godhead, appears separate from the living being but is actually separate and not separate simultaneously. This is the philosophy of acintya-bhedābheda-tattvapropounded by Śrī Caitanya Mahāprabhu. According to the reactions of karma, the living being appears separate from the Supreme Personality of Godhead, but actually he is very intimately related with the Lord.
(Srimad Bhagavatam----7:2:43----purport).

The word param means "the supreme cause," and aparam means "the effect." The supreme cause is the Supreme Personality of Godhead, and the effect is material nature. The living entities, both moving and nonmoving, are controlled by the Vedic instructions in art and science, and therefore they are all expansions of the external energy of the Supreme Personality of Godhead, who is the center as the Supersoul. The brahmāṇḍas, the universes, exist during the duration of a breath of the Supreme Lord (yasyaika-niśvasita-kālam athāvalambya jīvanti loma-vilajā jagad-aṇḍa-nāthāḥ (Bs. 5.48)). Thus they are also within the womb of the Supreme Personality of Godhead, Mahā-Viṣṇu. Nothing, therefore, is separate from the Supreme Lord. This is the philosophy of acintya-bhedābheda-tattva.
(Srimad Bhagavatam----7:3:32----purport).

When one is completely in knowledge of ahaṁ brahmāsmi, he thinks, "I am part of the Supreme Lord, my body is made of His material energy, and therefore I have no separate existence. Yet although the Supreme Lord is spread everywhere, He is different from me." This is the philosophy of acintya-bhedābheda-tattva. An example given in this regard is that of the aroma within the earth. In the earth there are aromas and colors, but one cannot see them. Actually we find that when flowers grow from the earth, they appear with different colors and aromas, which they have certainly gathered from the earth, although in the earth we cannot see them.
(Srimad Bhagavatam----7:9:35----purport).

Lord Śrī Kṛṣṇa and His plenary expansions are all in the category of the Lord Himself, the energetic Absolute Truth, whereas His devotees, His eternal associates, are His energies. The energy and energetic are fundamentally one, but since their functions are differently exhibited, they are simultaneously different also. Thus the Absolute Truth is manifested in diversity in one unit. This philosophical truth, which is pursuant to the Vedānta-sūtra, is called acintya-bhedābheda-tattva, or the conception of simultaneous oneness and difference. In the latter portion of this chapter, the transcendental position of Śrī Caitanya Mahāprabhu and that of Śrīla Nityānanda Prabhu are described with reference to the above theistic facts.
(Sri Caitanya Caritamrta-- 1:1:----summary).

The material world, full of conditioned souls trying to lord it over matter, is a manifestation of the external energy of the Supreme Lord, and the spiritual world, full of perfect servitors of the Lord, is a manifestation of His internal energy. Since all living entities are minute sparks of the Supreme Personality of Godhead, He is the Supreme Soul in both the material and spiritual worlds. The Vaiṣṇavas following Lord Caitanya stress the doctrine of acintya-bhedābheda-tattva, which states that the Supreme Lord, being the cause and effect of everything, is inconceivably, simultaneously one with His manifestations of energy and different from them.
(Sri Caitanya Caritamrta-- 1:2:37----purport).