vasamsi jirnani yatha vihaya
navani grhnati naro ’parani
tatha sarirani vihaya jirnany
anyani samyati navani dehi

Translation of Bhagavad Gita 2.22

As a person puts on new garments, giving up old ones, the soul similarly accepts new material bodies, giving up the old and useless ones.

Commentary by Sri A.C. Bhaktivedanta Swami Prabhupada of Gaudiya Sampradaya:

Change of body by the atomic individual soul is an accepted fact. Even the modern scientists who do not believe in the existence of the soul, but at the same time cannot explain the source of energy from the heart, have to accept continuous changes of body which appear from childhood to boyhood and from boyhood to youth and again from youth to old age. From old age, the change is transferred to another body. This has already been explained in a previous verse (2.13).

Transference of the atomic individual soul to another body is made possible by the grace of the Supersoul. The Supersoul fulfills the desire of the atomic soul as one friend fulfills the desire of another. The Vedas, like the Mundaka Upanishad, as well as the Shvetasvatara Upanishad, compare the soul and the Supersoul to two friendly birds sitting on the same tree. One of the birds (the individual atomic soul) is eating the fruit of the tree, and the other bird (Krishna) is simply watching His friend. Of these two birds—although they are the same in quality—one is captivated by the fruits of the material tree, while the other is simply witnessing the activities of His friend. Krishna is the witnessing bird, and Arjuna is the eating bird. Although they are friends, one is still the master and the other is the servant. Forgetfulness of this relationship by the atomic soul is the cause of one’s changing his position from one tree to another, or from one body to another. The jiva soul is struggling very hard on the tree of the material body, but as soon as he agrees to accept the other bird as the supreme spiritual master—as Arjuna agreed to do by voluntary surrender unto Krishna for instruction—the subordinate bird immediately becomes free from all lamentations. Both the Mundaka Upanishad (3.1.2) and Shvetasvatara Upanishad (4.7) confirm this:

samane vrkse purusho nimagno
’nisaya socati muhyamanah
justam yada pasyaty anyam isam
asya mahimanam iti vita-sokah 

“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.” Arjuna has now turned his face towards his eternal friend, Krishna, and is understanding the Bhagavad-gita from Him. And thus, hearing from Krishna, he can understand the supreme glories of the Lord and be free from lamentation.

Arjuna is advised herewith by the Lord not to lament for the bodily change of his old grandfather and his teacher. He should rather be happy to kill their bodies in the righteous fight so that they may be cleansed at once of all reactions from various bodily activities. One who lays down his life on the sacrificial altar, or in the proper battlefield, is at once cleansed of bodily reactions and promoted to a higher status of life. So there was no cause for Arjuna’s lamentation.Commentary by Sri Vishvanatha Chakravarthi Thakur of Gaudiya Sampradaya:

“But by my fighting, a jiva will give up the body known as Bhisma. Then you and I will be the cause of that.”

“What fault is there in a person giving up old worn cloth to put on new cloth? In a similar way, Bhisma will give up an old body and attain a new divine body. What fault is there for me or you in that?”Commentary by Sri Ramanuja of Sri Sampradaya:

2.22 That those who give up their bodies in a righteous war get more beauteous bodies than before, is known through the scriptures. Casting off worn-out garments and taking new and beautiful ones, can be only a cause of joy, as seen here in the world in the case of new garments. Once again Sri Krsna emphasises for easy understanding the indestructibility of the self, taught before: ‘Know that to be indestructible by which all this is pervaded’ (II.17) and confirms it thus:
Commentary by Sri Sridhara Swami of Rudra Sampradaya:

It may be submitted that although the eternal soul is not slain; yet and still reflecting on the total destruction of the physical body one might still grieve. To answer this it is being put forth that just as new physical bodies which are dependent on karma or reactions from one’s actions in a present life will surely continue; so there is no need for grief at the destruction of old, worm out bodies. This is the proper understanding.
Commentary by Sri Madhvacharya of Brahma Sampradaya:

In this verse the Supreme Lord clarifies the distinction between the physical body and the eternal soul by giving this succinct analogy.

Now begins the summation.

The living entities propensity of acquiring and discarding physical bodies is factually the process of birth and death and therefore should be understood as not deserving to be the cause of sorrow. Thus the Supreme Lord gave explanation was given to delineate this.
Commentary by Sri Keshava Kashmiri of Kumara Sampradaya:

Although by reflection it can be clearly understood that the soul is indestructible and not to be lamented for; yet and still the physical body is destructible. With the termination in battle of the physical body of a very dear one such as preceptor, protector or loved ones the seperation from whom will undoubtedly cause deep lamentation. To categorically clarify this misusage Lord Krishna explains that just as there is no grief when one discards old worn out garments and there is joy at accepting new garments in the same way the embodied soul discarding old worn out bodies joyfully accepts new ones. So if preceptors like Bhisma were to lose their body in this war of righteousness then they would receive a new and better physical body in their next life and it would be beneficial for them and not unfavorable.
Commentary by Sri Adi Shankaracharya of Advaita Sampradaya:

2.22 Yatha, as in the world; vihaya, after rejecting jirnani, wornout; vasamsi, clothes; narah, a man grhnati, takes up; aparani, other; navani, new ones; tatha, likewise, in that very manner; vihaya, after rejecting; jirnani, wornout; sarirani, bodies; dehi, the embodied one, the Self which is surely unchanging like the man (in the example); samyati, unites with; anyani, other; navani, new ones. This is meaning.
Commentary by Sri Abhinavagupta of Kaula Tantra Sampradaya:    

2.22 Vasamsi etc. just as a well – dressed person, on the destruction of his garment, gets himself dressed in another more suitable garment, and he does not perish on that account, in the same way the Self, dressed with different bodies [behaves].
Sanskrit Shloka Without Transliteration Marks:

vasamsi jirnani yatha vihaya
navani grhnati naro ‘parani
tatha sarirani vihaya jirnany
anyani samyati navani dehi
Sanskrit to English Word for Word Meanings:

vāsāḿsi — garments; jīrṇāni — old and worn out; yathā — just as; vihāya — giving up; navāni — new garments; gṛhṇāti — does accept; naraḥ — a man; aparāṇi — others; tathā — in the same way; śarīrāṇi — bodies; vihāya — giving up; jirṇāni — old and useless; anyāni — different; saḿyāti — verily accepts; navāni — new sets; dehī — the embodied.