You're out shopping. A woman comes up to you, and says, "Hi Brunhilde." You have to explain that you're not Brunhilde. "Oh my gosh!" she exclaims. "You look just like her." (By the way this anecdote only works if your name is, in fact, not Brunhilde.)
You've had a near brush with your doppelgänger: a double of you who is out there in the world, but who isn't you.
Lydia Kang, over at The Word is My Oyster, posted a brief consideration of the possible medical underpinnings of believing you've been doppelgängered and the "syndrome of subjective doubles" last week. It's fascinating reading.
Literally, the term means "double walker." In the ancient and medieval world, seeing a double of yourself was bad news. People reported seeing a ghostly double of a living relative, performing actions that the person him- or herself would perform shortly afterward. To this day, some people report seeing copies of themselves in their peripheral vision, in positions where no reflection is possible. On a recent episode of the Mysterious Universe podcast, a caller reported waking up in the middle of the night to find his girlfriend being choked by a shadowy figure. After he managed to dispel the figure, he asked her what she had seen and experienced. She said she'd been attacked by what appeared to be a monster - with her boyfriend's face.
Doppelgänger accounts are richly suggestive of all kinds of paranormal / alternative notions: the non-linear nature of time; the ability of thought forms to manifest in concrete reality; and the mimicry capabilities of spirits or dark entities, just to name a few.
The gothic writers in the late 18th century went nuts for the doppelgänger motif. The term was coined by one of them - Jean Paul, in his novel Siebenkäs, published in 1796. In gothic terms, the doppelgänger was often associated with a failure of a character's self-coherence, and a sign of impending insanity or loss of identity.