Om Purnam Aadaaha- "Aham Brahmaasmi"..

Om Pooranam aadaaha Poornam idam, 
Poornaat Poornam udachyate,

Poornasya Poornam aadaaya, 
Poornam eva avashishyate..

The meaning of this Shanti Mantra from the Isha upanishad is as simple as this
That is full, This is full
Fullness is born out of Fullness
When fullness is added or subtracted out of fullness
What remains is fullness indeed

In-fact it is no different than declaring
Aham Brahmaasmi
I am Brahma.

If one were to utter this statement as it is, uninitiated, unprepared; it appears as innocuous and as useless, if not silly, as the declaration made by a gentleman lying prostrate in his living room that he is standing atop the Mount Everest. It is indeed meaningless and crazy but however if
A man who has actually scaled the Mount Everest and is standing atop there with a flag of victory, when he declares that he is there, the scene is entirely different..

So one needs to understand that these Maha-Vaakyaas are the voice of the sages who are there.. and these words merely serve to stimulate the fellow human beings who are down there in the planes that there is a place called Mount Everest and it can verily be scaled, it is no imagination..

This Maha Vaakya is the voice of the realised one who has attained to Self Consciousness..
After the Atmic Reality wakes up it addresses itself as "this" and the worldly state and all else from which it rises is addressed as "that". and so does it declare that the Fullness that is Me has indeed arisen, not from any hollowness but from the Fullness which I hitherto mistook to be the world..
Only after one has tasted ones own fullness can one make a declaration such as this.. an ignorant suffering mind can not to be talking about fullness and fulfilment everywhere, all over..
It is the deathless eternal Atma alone who sees the deathless eternal Param-atma everywhere.

After one is established in Ones Own Absolute Fulfilment or The Self or Atma one says..

Poornaat Poornam Udachyate

Infinite Absolute Fullness has come out of The Infinite absolute Fullness

Shaashwat can not have arisen out of the (imaginary) Nashwar.
The Truth which is Me can not have risen out of the Untruth- the imaginary world..

It is infinite alone which gives rise to the infinite, 

and what remains is still infinite alone..

When gold ornament is made out of gold

What remains is gold only..

This wholeness which is Me has indeed come out of the Wholeness which is all around..

Gold and Gold ornament are one and the same, what is the distinction.

Do you have to dismantle the ornament to know that it is gold.

When a gold ornament is made out of gold

still it continues to be as much gold.
and it is Me (the Gold) alone who knows that it is Me (the Gold) alone all over.

It was My own illusionary momentariness called mind, which was seeing Myself (gold) to be the mere transitory ornament instead of seeing it as Me Myself (Gold itself).
It was the ignorant mind which hitherto saw Wholeness to be some imaginary Hollowness..

This Creation is the Creator Himself indeed, and
This is the first-hand experience of The (Realised) Soul..