The speaker/poet continues to bear the song sung by the solitary Scots lass because it sounds so sad and so beautiful. Sad melodies tend to be a bit more haunting than happy ones, and, despite the speaker's inability to understand the maiden, he can tell that it is a "melancholy strain" she sings. Her voice seems to fill up the vale and his soul, and it likely has such a profound effect, in part, because it is so heartrending.
Also, the fact that the speaker cannot understand the maiden's words seems to make the song stick with him longer so that he goes on remembering it even when he can no longer hear it. He asks, "Will no one tell me what she sings?" before he ponders many of the possibilities for the subject matter of the song. Had he known what she was singing about, the song would have lost its mystery and would, perhaps, not have stayed with him because it would not have stirred his imagination the way it does.