What is Prakṛti and Puruṣa in the Bhagavad Gita?
Prakṛti is nature: everything that changes, including your body, your senses and your mind. Puruṣa is the one who is aware of all that and is not itself part of the show. The pair comes from Sāṅkhya, the older system the Gita borrows from and then modifies.
Chapter 13 is where this is worked out, under the names field and knower of the field. Your body is the field. What knows it is the knower. 13.20 makes the division carry the explanatory weight: prakṛti is said to be the cause of everything that gets done, while puruṣa is the cause of the experiencing of pleasure and pain.
The practical use is smaller than the metaphysics and worth having. A great deal of what you treat as you is on the field side: the mood, the fatigue, the reflex, the appetite. None of those is nothing, and none of them is the one noticing them. Chapter 14 adds the part people miss, that even the clear and pleasant states belong to nature, which is why it says clarity binds too.
The verses 18
3.27
Everything that gets done is done by the forces nature is made of.
3.33
Even someone who knows better acts according to his own nature.
7.4
Earth, water, fire, air, space, mind, intellect and the sense of being someone - this is my nature, divided eight ways.
7.5
That is the lower nature.
7.6
All beings are born out of these two.
9.7
All beings go into my nature at the end of an age, Arjuna.
9.8
Presiding over my own nature, I send out again and again this whole crowd of beings - helpless, under the force of nature.
9.10
With me as the one overseeing it, nature gives birth to everything that moves and everything that does not.
13.19
So the field, and knowledge, and what is to be known have been told in brief.
13.20
Know that nature and the person are both without beginning.
13.21
Nature is said to be the cause in the matter of doing - of what is done and the means of doing it.
13.22
The person, seated in nature, experiences the strands born of nature.
13.23
And in this body there is also a higher person - the one who watches and permits, who supports, who experiences, the great lord, called the supreme self.
13.26
Others, not knowing in these ways, worship because they have heard it from others.
14.3
My womb is the great nature.
14.4
Whatever forms are produced in any womb, Arjuna, the great nature is their womb, and I am the father who gives the seed.
18.59
If you take shelter in self-importance and think I will not fight, your resolve is false.
18.60
Bound by your own work, Arjuna, which comes out of your own nature, you will end up doing helplessly the very thing you do not want to do now, out of confusion.