Purport

Happy with the devotion and purity of request by Arjuna, Shri Krishna agreed to reveal his prominent manifestation(Vibhuti). And here he reveals his first manifestation. Bhagvan Shri Krishna declares He(Shri Krishna) is the self(soul) placed in the heart of all living beings. Further he declares he alone is is the beginning, middle and end o all beings.

What declared here by Shri Krishna is not only the most important of all philosophies of Sanatan Dharma but also one of the most complexes for anybody to understand. Anybody who reads above words may get perplexed for a moment, how is this possible that Shri Krishan simultaneously exists in all living beings. Not able to understand a human can go on to form other questions. A human gets confused hearing these words is quite obvious as this is beyond human capacity to comprehend. But this is the most concepts, understanding which may suddenly makes everything clear to human.

To understand this fact one has to jointly study the concept of Bramhan, soul and life. As described in Chapter 14, Bramhan is the primeval potency of Bhagvan Shri Krishan spreading in whole universe like the ether(sky), A soul is but a one unit like a photon which always sustained and exists in the realm of Bramhan. Since Bramhan, one of the to main potencies of Bhagvan Shri Krishna, is eternal and that is why soul too is eternal(As explained in chapter 2, sh12-30).

The supreme Parmatma exists in every living beings is mentioned in almost every main scriptures,
The Brihadaranya Upanisad V.VII.XV
yas sarvashu bhuteshu tishthan sarvebhyo bhutebhyo

states: He who is enthroned in the heart of all beings, Who is the innermost of all beings, Whom all the beings know not, Whom all beings form His spiritual body, Who rules the interior of all beings, is the atma, the antaryami the immortal inner ruler.

In the same Upanisad (The Brihadaranya Upanisad V.VII.XXII)
ya atmani tisthan atmano
It states: He who is enthroned within the Atma, Who resides within the interior of the Atma, Whom even the Atma does not know, Whom all Atma's are the spiritual body, Who rules the interior of the Atma is Paramatma the Supreme Atma of all.

Other scriptures also explain this fact in different ways. This concept is one of the most important concepts for everybody to understand.