Of all the images in the Gita, this one has stayed in the memory of millions. Just as a person takes off worn-out clothes and puts on fresh ones, the soul discards old bodies and enters new ones. That is all death is — a change of garments.
The power of this metaphor lies in how ordinary it is. Every person alive has changed clothes. Nobody mourns the shirt they wore yesterday. Nobody fears the moment of taking it off. Krishna uses this everyday act to reframe the most feared event in human life. Death is not destruction. It is a change of covering.
Notice that the person changing clothes remains the same throughout. The shirt changes; the wearer does not. The body changes; the soul does not. This distinction — between the one who wears and what is worn — is the heart of everything Krishna has been teaching since shloka 2.11.