This article is written from the divine teachings of HDG AC Bhaktivedanta Swami Srila Prabhupada and by the mercy of His Grace Gauranga Sundar Das Gurudevji; completely dedicated to both of my spiritual masters.

Lord Kṛṣṇa states in Bhagavad-gita 15.7, mamaivāṁśo jīva-loke jīva-bhūtaḥ sanātanaḥ, The living entities in this conditioned world are My eternal, fragmental parts. Because we all are His part and parcels, we inherits the same quality as Lord Kṛṣṇa. It's just like a son inheriting his father's quality. Lord Kṛṣṇa is called as Sat-cit-ānanda, means full of eternity, knowledge and bliss. As the part and parcel of Kṛṣṇa, we naturally inherits such qualities. ajo nityaḥ śhāśhvato ’yaṁ purāṇo
na hanyate hanyamāne śharīre (BG 2.20).
The body is subject to six kinds of transformations. It takes its birth from the womb of the mother's body, remains for some time, grows, produces some effects, gradually dwindles, and at last vanishes into oblivion. But soul, however being the part and parcel of Kṛṣṇa, does not undergo any change. He is pure and steady (free from six types of changes). This steady nature of the soul is known as kūṭastha. kūṭastha means steady.
For the soul, there is never birth nor death, nor having once been, does he ever cease to be. Anything in the material world which took his birth has his death, but because the soul has never taken his birth, he does not die as well. He is beyond time. Soul is not subjected to the past, present or future. The concept of time applies to the body having taken its birth. And as we can see that the soul is free from the cycle of birth and death, is also free from the 4th dimension, time, namely as past, present or future. You can scram the whole history, you won't find any trace of soul coming into being. We as the individual, atomic souls have been present eternally along with Lord Kṛṣṇa.
Under the impression of the body, we seek the history of birth, death, etc of the soul. But the soul does not become old at any time, as the body does. This is the reason for the old man feeling the same spirit inside him as he was in childhood or youth. The changes of the body do not affect the soul. He has no by-product either. But because the body is producing some by-products, it appears to be his children, but in reality, all his children are eternal, fragmental souls of the Supreme Personality of Godhead, Kṛṣṇa.
One may then question about the growth or the changes that the body undergoes, how it happens if the body is simply matter. Absolutely, the body is simply matter but all the changes the body undergoes is on account of the soul being present within the body. It is because of the soul's presence, that the body undergoes such changes, but the soul himself is free from such offshoots or change.
Soul is always full of consciousness. Consciousness is the symptom of the soul. Even if one does not find the soul within the heart, where he is situated, one can still understand the presence of the soul simply by the presence of consciousness. Sometimes we do not find the sun in the sky owing to clouds, or for some other reason, but the light of the sun is always there, and we are convinced that it is therefore daytime. Similarly, the presence of the consciousness proves the existence of the soul. But the consciousness of the soul is different from the consciousness of the supersoul. Individual living soul is prone to forgetfulness. But Supersoul remembers everything. Supreme consciousness is of all knowledge- of past, present and future.
Since the atomic soul is forgetful of his original identity as Sat-cit-ānanda, he has to take the instructions from the Supreme Lord, Kṛṣṇa. Lord Kṛṣṇa is not forgetful like us, had He been on the same position, the whole teachings of Bhagavad-gita had been of no value. The whole Bhagavad-gita is based on this analogy where Arjuna is playing the part of the enjoying bird, who is forgetful of his original identity as part and parcel of Lord Kṛṣṇa and is now lamenting on the miserly weakness and bodily attachments, whereas Lord Kṛṣṇa, playing the role of the instructor is guiding Arjuna to come out of the ignorance and remember his original identity as his parcel. This analogy has been nicely explained in the Katha Upanishad as follows :
anor anīyān mahato mahīyān
ātmāsya jantor nihito guhāyām
tam akratuh paśyati vīta-śoko
dhātuḥ prasādān mahimānam ātmanaḥ
(Katha 1.2.20)
"Both the Supersoul [Paramātmā] and the atomic soul [jīvātmā] are situated on the same tree of the body within the same heart of the living being, and only one who has become free from all material desires as well as lamentations can, by the grace of the Supreme, understand the glories of the soul."
There are two souls present in the body, one is the individual soul and another is the Supersoul. Analogy given here is two birds are sitting on the same tree, one is enjoying the fruits of the tree and another friend is simply witnessing the bird enjoying. So, Supersoul is like the witnessing bird, and the individual atomic soul is like the enjoying bird. Supersoul present within the body is none other but the Supreme Personality of Godhead, Kṛṣṇa and we are just like the bird who is busy in enjoying the fruits of the karmas. Lord Kṛṣṇa, being so kind upon the atomic souls, accompanys him in every body birth after birth as the Supersoul and waits for him to turn towards Him and understand His glories. Even though they are friends, one is still the master and the another is still the servant. As soon as the enjoying bird accepts the other bird as the Supreme spiritual master, he immediately becomes free from all lamentations and all anxieties.
Both the Katha Upaniṣad and Śvetāśvatara Upanisad confirm this:
samāne vṛkşe puruşo nimagno 'nīśayā śocati muhyamānaḥ juştaṁ yadā paśyaty anyam īśam asya mahimānam iti vīta-śokah
"Although the two birds are in the same tree, the eating bird is fully engrossed with anxiety and moroseness as the enjoyer of the fruits of the tree. But if in some way or other he turns his face to his friend who is the Lord and knows His glories-at once the suffering bird becomes free from all anxieties.”