The only reason this very moment feels so real is because it borrows existence from you.
I really didn't understand what YouTube commentator meant by phrase it borrows existence from you. But you (or we) feel world as real because you (or we) are not yet realized (did not become a Jivanmukta) and still subjected to mind and senses.
For beginners of Advaita, this is the most confusing part. See World is real even according to Advait Vedanta? and three states of realities as per Advaita.
Whatever we see with eyes, feel with hands are just thoughts in our mind. This is what Swami Vivekananda says in commentary of 2nd Sutra, Samadhipada of Patanjali Yoga Sutra.
Naturally we see that the mind is not intelligent; yet it appears to
be intelligent. Why? Because the intelligent soul is behind it. You
are the only sentient being; mind is only the instrument through which
you catch the external world.
Take this book; as a book it does not exist outside, what exists
outside is unknown and unknowable. It is the suggestion that gives a
blow to the mind, and the mind gives out the reaction. If a stone is
thrown into the water the water is thrown against it in the form of
waves. The real universe is the occasion of the reaction of the mind.
A book form, or an elephant form, or a man form, is not outside; all
that we know is our mental reaction from the outer suggestion.
Matter is the “permanent possibility of sensation,” said John Stuart
Mill. It is only the suggestion that is outside. Take an oyster for
example. You know how pearls are made. A grain of sand or something
gets inside and begins to irritate it, and the oyster throws a sort of
enameling around the sand, and this makes the pearl. This whole
universe is our own enamel, so to say, and the real universe is the
grain of sand. The ordinary man will never understand it, because,
when he tries to, he throws out an enamel, and sees only his own
enamel. Now we understand what is meant by these Vrttis. The real man
is behind the mind, and the mind is the instrument in his hands, and
it is his intelligence that is percolating through it. It is only when
you stand behind it that it becomes intelligent.
What Swamiji says here is, if we see a book on table, we don't really know completely what is there on Table. What it appears on table is just a reaction in mind. For example, let's say person with some eye defect sees the book, he might perceive it differently and let assume on some hypothetical planet if those persons are majority, then it will be considered as "reality" on that planet. So, there is uncertainty regarding sight. Similarly, there is uncertainty regarding sense of touch too. Even mind is not independent as it depends on something external (consciousness or Atman) as after death brain (mind is subtle and brain is gross) stops working, as subtle body (has Manomaya Kosha) leaves physical body (Annamaya Kosha).
In books "Jewel in the Lotus: Deeper Aspects of Hinduism" and/or "Journey Continues: A Sequel To Apprenticed To A Himalayan Master", Sri Maheswaranath Babaji, direct disciple of Sri Mahavatar Babaji, explains logically to Sri M all above mentioned points of how there is uncertainty in touch, sight and even explains how color and mass are not intrinsic properties of an object.
He proves Senses depend on mind and mind depends on consciousness (which is called true self (Atman)). I can't post those arguments as they are too long to post here. Finally Babaji ends arguments with this statements (taken from book Journey continues):
It is this uncertainty about the actual nature of the objective world
that is termed as the great illusion. Only the mere existence of it
can be acknowledged, not the form in which it appears to exist. The
absolute reality behind these illusions might appear abstract, but it
is only abstract in the sense that it is beyond the reach of our sense
conditioned to the practical, yet illusory, needs of our day-to-day
According to the sages, this abstractness called Brahman is the only
true reality, the only true existence. Our intellect can go a step
further than our sense only to acknowledge and understand that the
Brahman cannot be intellectually grasped. That pure existence, behind
the insubstantiality of the world and constantly changing forms, is
realized only in deep meditation, beyond the intellect and the mind,
when thoughts have completely ceased.
Swami Vivekananda too says the same in commentary of above verse. He says when all thoughts in mind are stopped, we perceive or know ourselves as consciousness (true self) just like when ripples on lake are stopped, we can see base/support of lake.
The bottom of the lake we cannot see, because its surface is covered
with ripples. It is only possible when the rippled have subsided, and
the water is calm, for us to catch a glimpse of the bottom. If the
water is muddy, the bottom will not be seen; if the water is agitated
all the time, the bottom will not be seen. If the water is clear, and
there are no waves, we shall see the bottom. That bottom of the lake
is our own true Self; the lake is the Chitta, and the waves are the
Going further, it can also be proved whole universe and existence is in Atman and it is also corroborated by Adi Shankara in his first verse of Dakshinamurthy Stotram.
विश्वं दर्पणदृश्यमाननगरीतुल्यं निजान्तर्गतं
मायया बहिरिवोद्भूतं यथा निद्रया ।
यः साक्षात्कुरुते प्रबोधसमये
तस्मै श्रीगुरुमूर्तये नम इदं
The Entire World is Like a City Seen within a Mirror, the Seeing
happening within One's Own Being, It is a Witnessing happening
within the Atman, (the Witnessing) of the Externally Projected World;
Projected by the Power of Maya; As if a Dream in Sleep, One
Experiences this Directly (this Play of Maya) during Spiritual
Awakening within the Non-Dual Expanse of One's Own Atman,
Salutations to Him, the Personification of Our Inner Guru Who Awakens
This Knowledge through His Profound Silence; Salutation to Sri
So, unless we stop the thoughts in mind, we feel world as very real as we are under control of senses and mind.