Quantum interference is one of the most challenging principles of quantum theory. Essentially, the concept states that elementary particles can not only be in more than one place at any given time (through superposition), but that an individual particle, such as a photon (light particles) can cross its own trajectory and interfere with the direction of its path.
Debate over whether light is essentially particles or waves dates back over three hundred years. In the seventeenth century, Isaac Newton proclaimed that light consisted of a stream of particles; in the early nineteenth century, Thomas Young devised the double-slit experiment to prove that it consisted of waves. Although the implications of Young's experiment are difficult to accept, it has reliably yielded proof of quantum interference through repeated trials. The noted physicist Richard Feynman claimed that the essentials of quantum mechanics could be grasped from an exploration of the double slit experiment.
For this variation of Young's experiment, a beam of light is aimed at a barrier with two vertical slits. The light passes through the slits and the resulting pattern is recorded on a photographic plate. If one slit is covered, the pattern is what would be expected: a single line of light, aligned with whichever slit is open. Intuitively, one would expect that if both slits are open, the pattern of light will reflect that fact: two lines of light, aligned with the slits. In fact, however, what happens is that the photographic plate is entirely separated into multiple lines of lightness and darkness in varying degrees. What is being illustrated by this result is that interference is taking place between the waves/particles going through the slits, in what, seemingly, should be two non-crossing trajectories.
We would expect that if the beam of photons is slowed enough to ensure that individual photons are hitting the plate, there could be no interference and the pattern of light would be two lines of light, aligned with the slits. In fact, however, the resulting pattern still indicates interference, which means that, somehow, the single particles are interfering with themselves. This seems impossible: we expect that a single photon will go through one slit or the other, and will end up in one of two possible light line areas. But that is not what happens. As Feynman concluded, each photon not only goes through both slits, but simultaneously traverses every possible trajectory en route to the target -- not just in theory, but in fact.
In order to see how this might possibly occur, experiments have focused on tracking the paths of individual photons. What happens in this case is that the measurement in some way disrupts the photons' trajectories (in accordance with quantum theory's uncertainty principle), and somehow, the results of the experiment become what would be predicted by classical physics: two bright lines on the photographic plate, aligned with the slits in the barrier. Cease the attempt to measure, however, and the pattern will again become multiple lines in varying degrees of lightness and darkness.