When I first heard the song it seemed to be about some rich lady who bought her way into heaven. The line "your head is humming and it won't go, in case you don't know" seemed appropriate to the endless loop I was experiencing. But it took a long time for the story to come together in my mind.
As I got into it, there seemed to be a lot of non-sequiturs. Consider the line "in a tree by the brook, there's a songbird who sings, sometimes all of our thoughts are misgiven." Where did THAT come from? We were just talking about the Stairway lady. It made me wonder.
In time I realized the song is not a linear story. It's a series of images altered by the later context. It's kind of like a movie that starts in the middle of the story and only later supplies the context to understand what you've seen.