Bhagavad Gita Verse 6, Chapter 4

ajopi sannavyayaatmaa bhootaanaameeshvaropi san |
prakritim svaamadhishthaaya sambhavaamyaatmamaayayaa || 6 ||
 
Though I am beyond birth, imperishable and the controller of all beings, yet by commanding my nature, I manifest with my maaya.
 
ajaha : beyond birth
api : yet
san : though
avyayaatmaa : imperishable
bhootaanaam : among all beings
eeshvaraah : controller
san : though
prakritim : nature
svaam : my
adhishthaaya : commanding
sambhaavami : I manifest
aatmamaayayaa : with my maaya
 
This is an important shloka in the Gita, because Shri Krishna reveals himself as Ishvara, the controller of all beings. He says he is not born into this world like an ordinary human. He wills himself or manifests himself into existence by controlling prakriti, which is made up of the 3 gunaas. The power that causes this manifestation is called maaya. Let us look at two examples to understand this concept further.
 
Our body has billons of cells that carry our a wide range of functions. Each of these cells behave independently. But they are all working for an entity - the person - who is much larger and powerful than all of them put together.
 
Also consider the wave and the ocean. There are many waves, but all of them are part of a gigantic entity called the ocean. The ocean contains all the waves on the surface, as well as a vast quantity of water that lies under the surface. The wave derives its power from the ocean, but the ocean is more powerful than any one wave.
 
Similarly, the entire universe is the body of the supreme person known as Ishvara, who is the controller of the universe and the most powerful entity in existence. We are like waves that derive our power from the ocean called Ishvara. The power of Ishvara can be seen in the laws of nature, especially when we see cosmic phenomenon like a supernova explosion. The intelligence of Ishvara can be seen in the harmony of the universe, when we see the vast cosmos with stars, planets, the sun and so on.
 
Prakriti is related to both us and Ishvara but in different ways. While we are usually under the control of prakriti (the 3 gunaas), it is Ishvara that controls prakriti. It is like a wild horse controlling its rider versus an experienced jockey controlling a race horse. But both Ishvara and us are nothing but the eternal essence, just like the wave and ocean are made up of water. When the eternal essence identifies with a finite body, it is a jeeva. When it identifies with the entire universe, it is Ishvara.
 
Having grasped the concept of Ishvara, let us know look at the concept of "avataar" or manifestation. Let's say a small rat tries to invade a large ant colony. Immediately, the entire ant colony springs into action. It is as if there is an "ant colony intelligence" that commands ants to collectively attack the rat in order to protect the ant colony. There was no "birth" of that collective attack, it manifested in response to a situation, and ended as soon as the situation was dealt with.
 
Similarly, Ishvara has the ability to manifest in the universe. The manifestation could be a short-lived one, like one thought in a person's mind. It could also be long-living manifestation like a human being in the form of Shri Krishna. Our Puraanic literature describes several avataaras in great detail, but these are only a subset of the countless avataaras that take place over time. An avataara is like a rain-bearing cloud: it materializes out of thin air, does its work, and quietly disappears.
 
So why does Ishvara need to take an avataara? Shri Krishna covers this topic in the next two oft-quoted shlokas of the Gita.
 

Bhagavad Gita Verse 20, Chapter 2

na jaayate mriyate vaa kadaachinnaayam bhootvaa bhavitaa vaa na bhooyaha |
ajo nityaha shaashvatoyam puraano na hanyate hanyamaane shareere || 20 ||
 
It (the eternal essence) is neither born, nor does it ever die; nor is it that having come into existence, it will again cease to exist. It is birthless, eternal, changeless and primeval, it is not slain when the body is killed.
 
na : not
jaayate : born
mriyate : dies
vaa : and
kadaachita : ever
na : not
ayam : this
bhootvaa : having come into existence
abhavitaa : ceases to be
vaa na : it is not the case that
bhooyaha : again
ajaha : birthless
nityaha : timeless
shaashvataha : changeless
puraano : primeval
na hanyate : slain
hanyamaane : when slain
shareere : the body
 
This shloka reinforces the attributes of the eternal essence that we have seen so far, that it is eternal and changeless. Any material object, including the human body, goes through six types of modifications: birth, exist, change, grow, decay, and to perish. The eternal essence is beyond all these modifications, hence it is changeless.
 
Two additional qualities of the eternal essence are provided here. The first is that it is birthless. It is logical that it should be birthless, otherwise it could not be eternal and timeless. And since it is birthless, it would have always existed, therefore it is primeval.
 
Note the change in meter to highlight the importance of this shloka.
 
Footnotes
1. "Om namoji aadya" is the very first ovi or stanza of the Jnyaneshwari. Sant Jnyaneshwar invokes the primeval quality of the eternal essence by using the word "aadya" which means primeval.