Purport

Now Shri Krishna gives answers to the questions asked by Arjuna. Starting from these two Shlokas and onwards, Shri Krishna explains first by giving a short definition as in these Shlokas and then explains them in detail in subsequent Shlokas. The terms explained by Shri Krishna in these two Shlokas are as follows:

1. Kshetra( The field):
Shri Krishna explained the physical body of living beings is called Kshetra, the field.

In normal practice and communication, a piece of land is called “Kshetra”. The land is the surface of the earth. Earth is one celestial body among the billions in this physical universe. In short, a piece of land is just a small part of the physical world. In a similar manner, a living body is also a small abstraction of the same physical world.
On the spiritual ground, a physical body of a living being and a piece of land both are simply an abstraction of the physical world called Kshetra.

2 KshetraJna(Knower of the field)
The word meaning of “KshetraJna” is one who knows the Kshetra.

What exactly knower of the field and who can be the knower of the Kshetra(The physical body) is still not clear in these two Shlokas, what is very clear which is also mentioned in shloka #3 is that Lord Shri Krishna is the knower of all the fields(physical body of all living beings).

The only question that remains here, can the individual Atma(soul) also be the knower of the field(Kshetra or physical body)
Shri MadhvaCharya has declared soul can’t be the knower, his statement goes as follows:

“na ca jaIvasya xao~&naama – xao~& eta manasaao ivaBaUtIjaI-vasya maayaaricata Aina%yaa: | Aaivaih-taScaaip itraoihtacca Sauwao ivacaYTo (ivaSauwktu -: || [it ih Baagavato ||” - xao~& is not in reference to the Jiva. xao~& is one who being pure and beyond modifications is capable of creating, with his Will, in the waking state the actual and in the dream and dreamless states, the experiences subject to modifications and hence not eternal. Thus, in Bhagavat Purana.
--Shri Madhvacharya:
Shri Madhavcharya produces the evidence from Shri Bhagvattam to conclude that an individual soul can’t be the knower of the physical body(the field)

The Bhagavat Purana states that the word kshetra-jna applies to the Supreme Lord, who is transcendentally pure and beyond any modifications is capable of creating perfectly by His will alone in the waking state, the dream state, and the dreamless state. Anything contrary to Him is subject to modification and transitory and thus not eternal.
--Shri Madhvacharya commentary

Another Scholar ShriDhara Swami has similar views as Shri Madhavacharya. He writes as follows:

Now the non-transmigratory nature of the atma or eternal soul which is of the nature of ksetrajnam or consciousness within the physical body is being stated. This ksetrajnam is pervading the jiva and is verily the Supreme Lord Himself within all jivas as an infinitesimal fraction of His divine, immortal consciousness.
-- Shridhara swami

Both Ramanujacharya and Adi Shankaracharya are silent on whether an individual soul or any human being can be the knower of the field(Kshetrjna), however, Prabhupada claims an individual person can be the knower of the field(physical body)
his comments like this:

“Now, the person who does not identify himself with the body is called ksetrajna, the knower of the field”
--Prabhupada

Apart from Shri Prabhupada, the majority of the scholars conclude only supreme Lord Shri Krishna is the Kshetrajna(knower of the field).

Even though one accepts the view of Shri Prabhupada that one individual human being can be the knower of the field, it is still subject to meeting a condition and that is that if a person is enlightened enough to detach himself with his physical body. That means he is able to attain such a state where he does not identify himself with his physical body.

Another meaning which in my view can be derived from the word "Khetra-jna" is the master of the Khsetra(physical body). As described in Shloka#3, that Bhagavan Shri Krishna is the knower of all the fields. And we know he is the God of the entire universe and so he is the master of all living beings,

3. The highest knowledge:
To the question asked Shri Krishna declares the knowledge of both physical body(Kshetra) and Knower of the physical body(that is Supreme Lord Shri Krishna) is the ultimate or highest knowledge. Having knowledge of only one of two is partial knowledge.