This song doesn't appear to make much sense when the lyrics are studied closely, so many theories have popped up regarding the meaning (many of them concerning drugs).
Nik Kershaw had written the music but had no idea what the song was going to be about, so to practice the tune he added random lyrics to be used until he made the song properly, but he ran out of time and had to use the lyrics on the album.
He named the song "The Riddle" because that's essentially what it is.
