Targum Onkelos: to rule in the day and in the night, and to distinguish between light and darkness. And the Lord saw that it was good.
Rambam: to rule the day and the night through the astrological forces in the heavenly bodies, and to distinguish between the light and the darkness. God confirmed them in their existence in God’s will.
Ibn Ezra: “Day” begins at sunrise and “night” begins when three stars are visible. “Evening” begins at sunset and lasts for one and one-third hours and “morning” begins one and one-third hours before sunrise. Sunlight, thus, characterizes day and moonlight characterizes night. God understood that it was good.