It states in Tehillim (19:2) השמים מספרים כבוד א-ל ומעשה ידיו מגיד הרקיע, "The heavens recite Hashem's glory, and the sky tells of the work of His hands." When one looks up at heaven, one sees the sun, moon, stars, and the vastness of creation, recognizing Hashem's greatness and splendor.
The chapter uses the sun’s light as an analogy to the great light of the Torah. As it states (19:8-9) תורת ה' תמימה... מאירת עינים, "Hashem's Torah is perfect...enlightening the eyes." Rashi writes, "The Torah illuminates like the sun, as it states מאירת עינים, 'enlightening the eyes.'"
So, the sun reminds us of Hashem's endless greatness, and the sun reminds us of the bright light that's in the Torah. There are other essential lessons that one can learn from the sun.
One is that after the sun sets, it rises again. The Chofetz Chaim zt'l says that this reminds us that hard times will be followed by good times. The Chofetz Chaim bases his lesson on the following Gemara (Avodah Zarah 8.):
"The day Adam HaRishon was created, he saw the sun set and said, 'Oy! Because of my sin the world will become dark and return to be תהו ובהו, nothingness. This is my death sentence that was decreed on me.' He sat [in a fast], and he cried all night long, and Chavah cried opposite him. When the morning came, he said, 'It is the way of the world (מנהגו של עולם הוא), and he sacrificed an ox [as a korban todah]."
The Chofetz Chaim zt'l repeated this Gemara during the chaotic times and upheavals caused by World War One. He expressed that the next night, when Adam saw the sun set, he wasn't afraid. He knew that this was the way of the world. The sun sets, and then rises again. The Chofetz Chaim explained that people shouldn't lose hope due to the turmoil of the times. There have been hard times for Klal Yisrael in the past, but the sun shone for them in the end, and good times followed.
This lesson is very applicable to our times. Some people worry, "What will be the future of Bnei Yisrael?" We are encouraged by the knowledge that there were dark times in our past, but in the end, the sun shone, and it became good for Bnei Yisrael.
The Chasam Sofer zt'l (Toras Moshe, Chayei Sarah ד"ה ויגוע) discusses another message that we can learn from the sun. The sun teaches us that one only appreciates light and goodness when preceded by darkness. The Zohar (Tazria 47:) states, "If it weren't for darkness, one wouldn't appreciate the good of light." The same applies to the good of wealth or health and all other good aspects of life. One only appreciates them when he knows of the opposite.