Bhagavad Gita Verse 12, Chapter 2

na tvevaaham jaatu naasam na tvam neme janaadhipaaha |
na chaiva na bhavishyaamaha sarve vayamataha param || 12 ||
 
In fact, there was never a time when I did not exist, nor did you, nor did these kings; and never shall we all cease to exist hereafter.
 
tu  : in fact
na eva : certainly never
jaatu : any time
aham : I
na : did not
aasam : exist
na : nor
tvam : you
no : nor
ime : these
janaadhipaaha : kings
 
cha : and
na eva : certainly never
na : will not
bhavishyaamaha : exist
sarve : all
vayam : of us
ataha param : hereafter
 
The Gita uses a lot of poetic techniques, including using double negatives like the ones in this verse. If you cancel the double negatives, a simpler version of this verse will be "All of us are timeless and eternal. We always existed in the past, and we will always exist in the future".
 
This statement, at first glance, does not seem to make sense. So let's look at an example. Let's imagine a huge lake with deep waters. The surface of the lake is usually quiet. Once in a while, a wind blows across the lake causing a wave to appear for a few seconds, then disappear soon after.
 
If we apply the logic of this verse and examine it from the perspective of a wave, the lake always existed before the wave came into existence. And the lake will remain long after any wave has disappeared.
 
Similarly, an LCD television has thousands of pixels, or dots of light, on its screen. These pixels turn on and off, due to which a moving image is created on the screen. We can enjoy a movie on the screen that will begin and end, characters and situations will come and go, but the screen will remain as a constant.
 
Now, according to physics, matter can never be created or destroyed, it can only undergo change from one state to another. So therefore, this shloka reiterates this physical law by saying that the atoms and molecules that comprise us always existed in the universe in some shape or forms.
 
But, just like the surface of the lake is a constant that lets the play of waves happen on it, there is a timeless, eternal, constant surface or "essence" that is present in the entire universe, which is the backdrop on which the play of matter happens. 
 
At this point, what is being spoken of here may seem abstract and somewhat hard to conceptualize, but it is similar to algebra where we denote unknown quantities by variables like x and y, till such time as we deduce the right value.
 
Ok. So what exactly is this eternal essence? How do we see it? If it is present in us, which part of the body does it reside in?
 
Footnotes
1. The wave and lake example is from the Jnyaneshwari, which is filled with tons of examples to explain complex concepts such as this one.