Basically it's the author adoring someone else (whom he describes as a "beautiful dreamer" and the "queen of [his] song"). He tells her to "list" (=to listen) as he serenades her ("while I woo thee") with harmonious music ("with soft melody"). He says that (in his serenade,) all the noise and clatter ("life's busy throng") seem to disappear or become less important ("gone are the cares"). Then he tells her (the "beautiful dreamer") to wake up and see him ("awake unto me"). You can read more about the song on Wikipedia here: https://en.wikipedia.org/wiki/Beautiful_Dreamer :)

Beautiful dreamer, queen of my song, 美丽幻夢者, 我歌之后 List while I woo thee with soft melody; 聽着我微曲音求愛之 "list" 詩中 "listen" 的 略語 Gone are the cares of life's busy throng, 生命忙碌的憂慮, 去/逝 之 Beautiful dreamer, awake unto me! 美丽幻夢者, 為我而醒!

A throng is a large crowd of people. The construction "gone are..............." means that the subject in question is not present anymore. "To woo," means to try to gain somebody's love. With this information you can probably deduce the rough meaning of this verse...

Perhaps you could tell us what you think they mean first and we could then comment.