Bhagavad Gita Verse 18, Chapter 15

yasmaatksharamateetohamaksharaadaapi choottamaha |
atosmi loke vede cha prathitaha purushottamaha || 18 ||
 
For, I transcend the perishable and also am superior to the imperishable. Therefore, in the world and in the Vedas, I am well known as the foremost person.
 
yasmaat : for
ksharam : perishable
ateetaha : transcend
aham : I
aksharaat : imperishable
api : also
cha : and
uttamaha : superior to
ataha : therefore
asmi : I am
loke : in the world
vede : in Vedas
cha : and
prathitaha : well known
purushottamaha : foremost person
 
Now, Shri Krishna reveals his true identity as Purushottama, the uttama Purusha, the foremost person, which is a poetic means of referring to the eternal essence, the pure brahman without any limitations. The root of the sanskrit word "uttama" is "ut" or high. This means that there is nothing higher than Purushottama. The imperishable, also known as Prakriti or Maaya, could be considered superior to the perishable world, because Prakriti is the cause and the world is its effect. Any cause is superior than its effect, just like the parents are superior to their children. Since Prakriti exists only as an adhyaasa, a projection on Purushottama, he is greater than anything else.
 
Let us also look at the significance of Purushottama by going deeper into what is meant by cause and effect. According to Vedanta, there are two types of causes. The material cause is the substance which makes the effect. A clay pot is made of clay, so its material cause, its upaadaana kaarana, is clay. But the pot did not make itself. There was an intelligence in the form of a potter that created the clay pot. This is the second type of cause is the nimitta kaarana, known as the intelligent or efficient cause.
 
Some schools of thought assert that the Purushottama is only the intelligent cause and not the material cause. He is like the potter who is distinct and separate than his creation. But in the Advaita school, the Purushottama is not only considered the intelligence behind creation, he is also the raw material behind the creation. The Mundaka Upanishad compares Purushottama to the spider who weaves the web from within himself, and eventually, pulls back the web into himself.
 
We should again not forget that this uttama Purusha, this foremost person, is nothing but our own self, our "I". In fact, uttama Purusha in Sanskrit grammatically means the first person, the "I". He is beyond the perishable tree of samsaara, and also beyond the seed of this tree in the form of Prakriti. What is the result of knowing this uttama Purusha? We will see in the next shloka.

Bhagavad Gita Verse 17, Chapter 15

uttamaha purushastvanyaha paramaatmetyudaahyataha |
yo lokatrayamaavishya bibhartyavyaya eeshvaraha || 17 ||
 
But distinct is that foremost person, spoken of as the supreme self, the imperishable lord, who enters and sustains the three worlds.
 
uttamaha : foremost
purushaha : person
tu : but
anyaha : distinct
paramaatma : supreme self
iti : in this manner
udaahyataha : spoken of
yaha : who
lokatrayam : in three worlds
aavishya : enters
bibharti : sustains
avyayaha : imperishable
eeshvaraha : lord
 
As we saw earlier, a single video game program can create an infinite variety of complex worlds in the computer. Let us now pose the question - what is the core, what is the essence of these complex worlds? What is the purest state of these worlds? We need to peel the layers of an onion, as it were. The worlds are not real, they are created by a computer program. A computer program is not real, it is a series of instructions in a computer’s memory. The instructions are not real, they are modifications of electricity. Ultimately, it is electricity that is creating and sustaining all of the worlds we see in a computer game.
 
Now, what if we pose the question - what is at the core of this world? If we get rid of all the limitations, what the purest state of this world? What is the purest state of our existence? The visible world is not real, because it is created by a play of the gunaas of Prakriti, and is perishable. Prakriti or Maaya is not real, though it is relatively imperishable, because it can be destroyed upon removal of our ignorance. What remains, is the eternal essence on which Maaya projects all its limitations or upaadhis.
 
Similarly, if we mentally remove our upaadhis or limitations, it will go something like this. Our body is a play of the gunaas, it is not real. Beyond the body are the senses and the mind, and they are comprised of gunaas and therefore not real. Beyond the senses and mind lies the eternal essence, untainted by Prakriti, which is the purest form of our “I”. In other words, when we remove all of our upaadhis or limitations, we come to the same eternal essence that is reached when we remove the upaadhis of the visible world.
 
We had seen the identity of our “I” with the eternal essence, of aatman with brahman, in the thirteenth chapter as well. That very same eternal essence, the purest brahman or shuddha brahman is referred to as the imperishable lord in this shloka by Shri Krishna. The three worlds here refer to either heaven, earth and hell, or even our waking, dreaming and sleeping states. The eternal essence enters and sustains all of them, but it is not some remote entity. It is the supreme self, the “I” residing within everyone.