O’Arjuna, “that which is unreal is non-existent; and that which is real cannot be non-existent.                                                      
An individual who sees the essence of both is called a wise man..”

First we should know what is unreal and real. Unless you know what is unreal and real you cannot move to the next stage of understanding. There is another problem in understanding..
To know unreal as unreal. you should know what is real. Yess, without knowing the real how can you know the unreal then.
To know real as real, you should know what is unreal. Now, it puts you in dire straits that you should know either to know another. 

what is unreal?
Unreal which has no past
Unreal has to be in the present 
Unreal should not have future.
This condition made clear that the Unreal is falls into the category of time

Then what is real?
Real is past, 
Real is present and 
Real is future. It is always present irrespective of time. 

Once you know the real then you know the unreal. Then you interpret the given situation. The situation is war, Arjuna afraid to kill Bhishma,  Dronacharya..etc. Actually, they are nothing but forms. they were not before or after. hence they fall into unreal but their Souls are not unreal but real.
Hence, you come to the conclusion “the Soul is Real and the Form is Unreal”. 

Now you understood 
The unreal can be killed and by killing the unreal, you never killed the real, that is soul. 
Hence Krishna telling Arjuna you are going to kill the unreal ie Body and you cannot kill the Soul of that person. 
If you know what is real and unreal. You are balanced and wise. 

Right now,
Balance is needed to tolerate today’s World, To understand balance, you need to move in between the two polarities otherwise you will judge one against the other because one is living inside the other. It’s like you calling your staff an idiot and he immediately changed and corrected. Now he is no more an idiot and he has become intelligent. he is carrying his intelligence on subsequent works.and now, you called him smart. After a few days, he made the same mistake and became an idiot. Now you tolerate him and continue to employ him because his nature is not a permanent idiot. The understanding is balancing and you stand to be a wise man.