The "double slit" or two slit experiment is a classic demonstration of how physics can act in ways counter to common expectations.
The basic set up of the experiment is simple, a laser is placed so that it shines onto an opaque screen with two close, narrow, parallel slits cut into it. A second, matte screen is put behind the first so that the light cast by the laser through the slits is projected onto it.
In many ways light acts like a wave. As the coherent light from the laser passes through the narrow slits it is diffracted into two spreading frustums (like a pair of trapezoids with their narrow ends at the slits). The second screen is set up to be far enough from the first that the two projections cross before reaching it. The two waves interfere constructively and destructively and a ripple-like pattern is cast onto the second screen.
At first glance this is a nice demonstration of the wave nature of light. The interesting part of this experiment occurs when you consider the wave/particle duality of light. Light can also be considered as a stream of quantized particles. That is, you can look at light (yeah, I know) as being made up of indivisible equal packets called photons.
This theory of light doesn't seem to conflict with the experimental results; The stream of photons produced by the laser is blocked by the screen, except at the slits where it spreads out by ricocheting off of their edges, and the two spreading streams of photons emerging from the slits interfere with each other as they collide, producing the same results. However if an electron gun is used to fire photons at the screen one at a time, and a light sensitive surface such as a photographic plate is placed in front of the second screen to record where each photon hit, an interference pattern develops, identical to the one produced when the photons are sent out in a stream.
This represents an enigma. If only one photon is being sent out at a time then there are never two streams of photons to interfere with each other. Some physicists believe that photons in parallel universes are interfering with the serially released photons. These are of course being fired by alternate experimenters. Others believe that this represents a failure in quantum theory.