I was in this experimental geometry class, where the students were supposed to work in groups and help one another learn theorems and whatnot, and the instructor was only there to babysit. As part of the "learning and discovery process," we were allowed to play music. It was a misguided disaster that reeked of hippie kum ba yah-ness. No one knew what the hell was going on. Redneck football players who could barely write their names were trying to learn about Pythagoras from homegirls who just wanted to talk about nails and hair.
But at least there was the music. And this one girl kept bringing in old Bowie albums on CD, and each one was like some new door opening. It was the first time I'd heard Ziggy Stardust and that raunchy little awwwww wham bam thank you, mam! chant in the middle of "Suffragette City." There also was the album The Man Who Sold the World (1970), and I instantly recognized that Mick Ronson riff from Nirvana's MTV Unplugged in New York set. When that special aired on MTV, I had just assumed that it was some obscure Pixies or Meat Puppets song that Kurt Cobain had decided to cover.
In all, it's a song about searching for your true self. Bowie uses the concept of a man who meets his doppelganger and then spends the rest of his days simultaneously running from/searching for him as a metaphor for self exploration/self-acceptance.
It was a perfect and chilling cover for Nirvana, considering Cobain's personal struggles and death by his own hand a few months later, and a very telling, personal tale from a young David Bowie, who would continue to explore his real identity (David Jones) in light of his public and stage persona(s) (David Bowie, Ziggy Stardust, The Thin White Duke, etc.) for many years.