Wave-Particle Duality of Matter: Matter in its finest state is observed as particles (electrons, protons, quarks), but when unobserved (such as moving from place to place) is described by waves of probability.
In this animation we imagine 20 electrons (or photons) that are fired in the direction of two slits in a barrier. As a single electron moves unobserved from place to place, it is described by a probability wave packet. The amplitudes of probability waves tell us where an electron is likely to be observed (large amplitude) and where it is not likely to be found (small amplitude).
Observe the pattern of interference that is created as the probability waves pass through the slits and into the region behind. As the waves pass over the pointing hands, regions of constructive and destructive interference of the probability waves are identified.
When the waves strike the screen, a remarkable thing happens! The waves collapse to a point and the electron is observed to strike the screen at a particular point as a particle would. That is why we say that an electron is always observed as a particle. The amplitudes of the probability waves tell us all of the possible places where an electron might be observed and the associated probabilities, but the spot where any particular electron lands cannot be predicted. (Watch several electrons pass through and be observed on the screen. You can't predict where the next one will hit!) The hits favor the high probability regions (constructive interference), so that if you watch many, many electrons pass through the system, they map out the regions of constructive and destructive interference of the waves. After twenty electrons, you will see the spots where they hit beginning to form groupings favoring the regions of constructive interference.