Kapila Muni is accepted as an incarnation of the Supreme Personality of Godhead, Kṛṣṇa. Here the word ādyaḥ means "the origin of all living entities," and puṁsām īśvaraḥ means "the Lord (īśvara) of the living entities" (īśvaraḥ paramaḥ kṛṣṇaḥ (Bs. 5.1)). Kapila Muni is the direct expansion of Kṛṣṇa, who is the sun of spiritual knowledge. As the sun dissipates the darkness of the universe, so when the light of the Supreme Personality of Godhead comes down, it at once dissipates the darkness of māyā. We have our eyes, but without the light of the sun our eyes are of no value. Similarly, without the light of the Supreme Lord, or without the divine grace of the spiritual master, one cannot see things as they are.
(Srimad Bhagavatam----3:25:9).

Īśvara, the Supreme Lord, Kṛṣṇa. Īśvara means the Supreme, īśvara means controller. But the supreme controller is Kṛṣṇa. Īśvaraḥ paramaḥ kṛṣṇaḥ (Bs. 5.1). Control everyone of us, we are controller. We control our family, our society, our business, our factory. There are different kinds of controller. So in that sense everyone is īśvara, but different types of īśvara. But the supreme īśvara.... Supreme means nobody controls Him, but He controls everyone. That is Supreme. Here we are controller, but we are also controlled, somebody else, superior than me. Therefore we cannot be called supreme controller. Supreme controller is Kṛṣṇa.
(Lecture on Bhagavad-Gita---1:15).

Īśvaraḥ paramaḥ kṛṣṇaḥ (Bs. 5.1). Īśvara means controller, one who controls. So everyone has got some capacity to control, every one of us. You are also controlling your family, controlling your business, and I am controlling this institution, and so on, so on. Everyone has got some. In that sense everyone is īśvara. There is no fight on this point. But we are controller of a limited circle, but we are controlled also. That is our position. Not that I am simply controller but I am controlled by higher authority. So therefore I am not supreme controller. I am controller, īśvara, but here is one, īśvara, Kṛṣṇa, īśvaraḥ paramaḥ. He is supreme controller. Why supreme controller? Because he is not controlled by anyone. That is Kṛṣṇa's position.
(Lecture on Bhagavad-Gita---3:27).

In the Brahma-saṁhitā it is said, īśvaraḥ paramaḥ kṛṣṇaḥ (Bs. 5.1). Īśvara means controller or the powerful man who controls. Take for example the president or the king. So there are many īśvaras, or controllers. You are also īśvara; I am also īśvara. Because you also control at least your family members or some animals. So this controlling capacity is there in everyone because we are part and parcel of Kṛṣṇa. But we are not supreme controller. We are controller of some entities, but we are controlled also by something superior. Therefore we are not absolute controller. We are relative controller. But about Kṛṣṇa, it is said, īśvaraḥ paramaḥ kṛṣṇaḥ (Bs. 5.1). Paramaḥ means supreme. He controls everyone or everything, but He is not controlled by anyone. That is īśvaraḥ paramaḥ.

(Lecture on Srimad Bhagavatam----1:2:6).