The lyric "Look into my eyes" in the song "The Sun" means to express love, which is as warm as the sun. Eyes are the windows of the soul. When you look in, you can see each other's hearts and express their deep love and trust.
Lyrics excerpts from "The Sun": You look into my eyes, you remember my voice, you March forward bravely in the storm, don't forget that I am standing here, you always feel lonely and depressed.