I like the famous song. But I can't understand what does "to promise the earth" mean. Does she want to give the Earth to him? I suspect native English speakers find it a strange question. Maybe I don't know all meanings of 'promise'. Could anyone explain to me this line?
This is a standard idiom in English. The earth here is a metaphor that symbolizes the impossible, the immoderate, or the unfulfillable:
The origin of this idiom is probably from the third temptation of Jesus (in the Bible), where the devil tempts him with the ridiculous promise of all the kingdoms of the world: