Bg 13.1-2 — Arjuna said: O my dear Kṛṣṇa, I wish to know about prakṛti [nature], puruṣa [the enjoyer], and the field and the knower of the field, and of knowledge and the object of knowledge. The Supreme Personality of Godhead said: This body, O son of Kuntī, is called the field, and one who knows this body is called the knower of the field.
Bg 13.3 — O scion of Bharata, you should understand that I am also the knower in all bodies, and to understand this body and its knower is called knowledge. That is My opinion.
Arjuna is asking about 6 questions from Krsna 1. Prakriti (nature) 2. Purusa (enjoyer) 3. Field (Ksetra) 4. Knower of the field (Ksetra-jnam) 5. Knowledge (Jyanam) 6. Object of knowledge. (Jneyam)
Field is the body, the material body is called ksetra why is it called? What happens in the Ksetra - variety of activities being performed in the ksetra. The conditioned soul wants to enjoy the material nature and it provides the body (8.4 million types of bodies - based on different sense gratification desire). Hence field is the body. Ksetra-jnam is the knower of the field - why is it important to know that the knower of the field is Krsna. The purpose of knowing the body is that Krsna knows the body and unless we know why the body is there for the purpose of self realization. The only purpose of this body is only to Go Back Home, Back to Godhead - We need to do brahma jignasa. The field of activity is to engage in KC.Krsna the knower of the field, the body, is always ready to give us direction to understand the knowledge that we are the soul, not the body and Krsna is the master, we are eternal souls and our only purpose is to serve Krsna. From verse 8 he is going to expand on the knowledge feature.
Bg 13.4 — Now please hear My brief description of this field of activity and how it is constituted, what its changes are, whence it is produced, who that knower of the field of activities is, and what his influences are.
Why is Arjuna asking these questions after Chapter 12 - Devotional Service? Knowledge of BG is a progressive knowledge. It is a sandwich - 1st 6 and last 6 are covering and middle 6 are the inside of the sandwich the core. The inside 6 are the nectar guarded by the coverings. Again from 13 he talks about the living entity and how he is transmigrating from one body to another. Arjuna is again bringing the question how the Jiva is interacting with prakriti, the material world and without this topic we won't be able to follow devotional service. Through these different element they help us plan our KC properly to seek more clarification about all of this so once these topics become clear then he is able to focus on devotional service and make concrete progress everyday. The various qualities/attributes I need to develop, what I need to focus on and how this all ties into the devotional service. The reason why the confidential chapters are in the middle is because it always needs to be protected and only now after attracting Arjuna did he want to now discuss these topics. Also, only now Arjuna is ready to understand these topics. Hence we now have chapters 13 where Arjuna is asking these questions.