In fact we are the soul inside our body & this soul can never die though body may die. As per the 'Bhagwat Gita', our body is like our clothes that we wear on our body & after death these worn out clothes are dropped by the embodied soul. In that sense your body is the Overcoat of your soul inside. You in essence are a 'Soul' & this 'Soul' of yours shall wear another body (read, shall wear another pair of clothes / Overcoat) after death. So this eternal soul is indestructible which changes its present embodied form/body for another embodied form/body, when the physical body dies.
Below are some verses of 'Bhagwat Gita' which explains the same truth.
First one is "Verse - 22, Chapter Two of Bhagwat Gita"
“vasansi jirn-nani yatha vihaay
navani grihnati naro-parani
tatha sharirani vihaya jirnany-
anyani sanyati navani dehi” (Gita: Chapter II verse 22)
"As a person discarding worn-out clothes, puts on new garments, likewise the embodied soul, casting off worn-out bodies,enters into other bodies which are new."
Second one is "Verse - 23, Chapter Two of Bhagwat Gita"
“nainum chindanti shastrani
nainum dahati pavaka
na chainam kledayanty-apo
na soshayati maruta” (Gita: Chapter II verse 23)
"Weapons cannot cut the soul, nor it can be burned by fire, nor water can moisten it, nor wind can make it dry."
Third one is "Verse - 24, Chapter Two of Bhagwat Gita"
akledyo-asoshya ev ch
nity sarv-gatah sthanur
achalo-ayam sanatanah” (Gita: Chapter II verse 24)
"For this individual soul is incapable of being cut; and insoluble, and can be neither burned nor dried. This soul is eternal, constant, omnipresent, unchangeable, immovable and everlasting."
Fourth one is "Verse - 30, Chapter Two of Bhagwat Gita"
“dehi nityam avadhyo-ayam
dehe sarvasy bharat
tasmat sarvani bhutani
na tvam shochitum-arhasi” (Gita: Chapter II verse 30)
"O descendant of Bharata, this soul residing in the bodies of all can never be slain. Therefore you should not grieve for any living being."
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