I was asked by a friend to describe what achintya-bhedaabheda-tattva (inconceivable simultaneous dual/non-dualism) means. Here's my attempt to explain Vedic conclusions in my own words...
Enjoy!

When analysing reality philosophically, there are 3 main conclusions people usually come to...
1. Nothing exists, ultimate reality is a void and what we experience here is totally illusory. We don't really exist.
2. Everything is One. Duality is illusory, in truth everything is homogenous with no distinctions.
3. Duality exists as an eternal principle of ultimate reality.

Most people think that since form and personality exist in the material world, they must not exist in the spiritual world. But an intelligent person may realise that option 1 cannot be true, because here I am existing... how does something come from nothing?
Number 2 is tricky. It sounds right, but... for the One to experience separation & distinction as we do, a 2nd factor necessarily needs to be involved. I'll explain: Oneness philosophers maintain that we're all one, but a tiny particle of that Oneness (you & me) somehow or another becomes covered by a 'cloud' of illusion that creates a subjective perspective of being separate from Source and distinct from each other. This philosophy sounds pretty cool and most people go for it. However, it's also flawed. The 'cloud' of illusion that creates separation must be something OTHER than Oneness itself, because Oneness has no defining qualities by which to create a sense of separation. By definition Oneness has no distinctions, so there cannot be Oneness plus clouds. That would make it Two!
In fact, oneness cannot be aware that it exists (because if it did then there would be TWO things, itself and its awareness of itself), and Oneness without awareness of itself doesn't exist, because who would be there to percieve it? If it's not being percieved, for all intents and purposes it doesn't exist. So in the end, Oneness philosophy is practically the SAME as Nothing/Void philosophy.
None of this explains the fact that we obviously exist.
So, because we seem to be existing, duality as an aspect of absolute reality needs to be considered.
The Vedas state that the variegatedness and duality we experience in the temporal material realm (including the etheric planes) is the reflection of a realm composed of similar items of absolute substantiality. A spiritual world.
Analogy: if you stand on the bank of a river and observe the reflection of a tree, one assumes the real thing exists independent of the reflection.
So the spiritual world, being the unconditioned and independent source of its reflection, matter, is described as a place of eternity, full knowledge, bliss, form, activity & desire centred around Godhead, who's the whole & centre of everything whilst simultaneously an independent personality.
The Sri Isopanisad explains: The Personality of Godhead is perfect and complete, and because He is completely perfect, all emanations from Him, such as this phenomenal world, are perfectly equipped as complete wholes. Whatever is produced of the Complete Whole is also complete in itself. Because He is the Complete Whole, even though so many complete units emanate from Him, He remains the complete balance.
Godhead's energies, relationships, forms, qualities, pastimes and entourage are unlimitedly variagated. The material world fractionally reflects and represents these eternal principles of the spiritual world, our constitutional home, not a formless blinding white light. Non-duality DOES exist, but as a secondary (subjective) aspect of Divinity. It's known as brahman and emanates from the Godhead, permeating everything.
In reality there IS only 1 thing: REALITY! And that reality is composed of duality: God & God's energies (including us and this world).
Below is a purport from the Sri Isopanisad to support these statements.

In the Bhagavad-gita (14.27), the Lord explains His personal rays (brahmajyoti), the dazzling effulgence of His personal form, in this way:
brahmaṇo hi pratiṣṭhāham
amṛtasyāvyayasya ca
śāśvatasya ca dharmasya
sukhasyaikāntikasya ca
"I am the basis of the impersonal Brahman, which is immortal, imperishable and eternal and is the constitutional position of ultimate happiness."
Brahman, Paramātmā and Bhagavān are three aspects of the same Absolute Truth. Brahman is the aspect most easily perceived by the beginner; Paramātmā, the Supersoul, is realized by those who have further progressed; and Bhagavān realization is the ultimate realization of the Absolute Truth. This is confirmed in the Bhagavad-gītā (7.7), where Lord Kṛṣṇa says that He is the ultimate concept of the Absolute Truth: mattaḥparataraḿ nānyat. Therefore Kṛṣṇa is the source of the brahmajyoti as well as the all-pervading Paramātmā. Later in the Bhagavad-gītā (10.42) Kṛṣṇa further explains:
atha vā bahunaitena
kiḿ jñātena tavārjuna
viṣṭabhyāham idaḿ kṛtsnam
ekāḿśena sthito jagat
"But what need is there, Arjuna, for all this detailed knowledge? With a single fragment of Myself I pervade and support this entire universe."
Thus by His one plenary expansion, the all-pervading Paramātmā, the Lord maintains the complete material cosmic creation. He also maintains all manifestations in the spiritual world. Therefore in this śruti-mantra of Śrī Īśopaniṣad, the Lord is addressed as pūṣan, the ultimate maintainer.

"The network of transcendental rays emanating from His body forms the splendrous light known as the Brahman effulgence, which is powerful enough to amaze the entire collection of material universes. If any of the conditioned souls desire to become content by merging into that glowing light, then that would be just like being satisfied at night with the glow of lightning bugs in the absence of the sun." -Bhaktivinode Thakura