(c) Jacob West

"Here a light source emits a photon along a path towards a half-silvered mirror.  This mirror splits the light, reflecting half vertically toward detector A and transmiting [sic] half toward detector B.  A photon, however, is a single quantized packet of light and cannot be split, so it is detected with equal probability at either A or B.  Intuition would say that the photon randomly leaves the mirror in either the vertical or horizontal direction.  However, quantum mechanics predicts that the photon actually travels both paths simultaneously! ... This effect, known as single-particle interference, can be better illustrated in a slightly more elaborate experiment, outlined in figure b below:"¹

(c) Jacob West

"In this experiment, the photon first encounters a half-silvered mirror, then a fully silvered mirror, and finally another half-silvered mirror before reaching a detector, where each half-silvered mirror introduces the probability of the photon traveling down one path or the other.  Once a photon strikes the mirror along either of the two paths after the first beam splitter, the arrangement is identical to that in figure a, and so one might hypothesize that the photon will reach either detector A or detector B with equal probability.  However, experiment shows that in reality this arrangement causes detector A to register 100% of the time, and never at detector B!"²

"This is known as quantum interference and results from the superposition of the possible photon states, or potential paths.  So although only a single photon is emitted, it appears as though an identical photon exists and travels the 'path not taken,' only detectable by the interference it causes with the original photon when their paths come together again.  If, for example, either of the paths are blocked with an absorbing screen, then detector B begins registering hits again just as in the first experiment!  This unique characteristic, among others, makes the current research in quantum computing not merely a continuation of today's idea of a computer, but rather an entirely new branch of thought.  And it is because quantum computers harness these special characteristics that gives them the potential to be incredibly powerful computational devices."³

Power and Potential of Quantum Computing

^1,2,3Figures and explanation borrowed from here.^*

*Because my head already hurts enough without trying to paraphrase this.