Humans intuitively understand a world defined by relatively large scales (km, m and cm), on which the “regular” forces, described by Newton's laws, work properly and succeed to describe various phenomena that occur in nature. But when we look at molecules and atoms, we enter into a world with very small scales; there the particle behavior is not compatible with the regular forces, the intuitive ones. Quantum mechanics describe phenomena that occur in the small scales.
First, in order to understand quantum mechanics we need to understand the building blocks of classical mechanics, which divide our world into two types of effects: effects of particles and effects of waves. Particle is characterized by mass or energy, the particle occupies a finite volume (defined borders) and is described by its location and time. Wave is disturbance that travels through space and matter according to the waves’ equation and described by wave length (which determines the frequency) and wave amplitude (the wave height).
Laws of classical mechanics, used to describe many phenomena until the early 20th century, for example, one of those phenomena is when shooting particles through a single crack, we get a typical particles’ pattern, a mark for places where particles pass through the crack and hit the wall (single stripe); therefore we respectively guess that when we will shot particles through two cracks we need to see two stripes. But in the 60s, scientists conducted an experiment in which electrons, which until then were defined as pure particles, were shoot through one and two cracks. Through the single crack, they saw a single stripe as expected, but in the case of two cracks, they saw interference and diffraction phenomena, fitting to behavior of waves. From the experiments they concluded that particles can also have wave’s features.
Large objects, like humans also have wave’s features, however since this is a large scale (macroscopic) the waves are not distinguishable. Quantum mechanics explain that, you can refer to any object of any size, like a wave under certain conditions and like a particle on other terms; this is called wave - particle duality.
Another confusing phenomenon was observed in the experiment with two cracks: when they added a measuring device to check from which crack the particle passed through, instead of receiving interference and diffraction pattern of a wave as before, they got two stripes, which corresponds to particle behavior. You can think the electron was aware of the measurement device and subsequently returns to behave as a particle. But basically, in order to perform the measurement, the measuring instruments performed with the electron interaction and thus affect the experiment and caused to the collapse of the interference pattern.
This experiment, together with additional experiments led to the development of quantum mechanics theory. In order to develop this theory scientists have to put away a fundamental principle in physics, determinism, which means, repeating the same experiment several times under the same conditions would lead to the same result. Quantum mechanics discard this view, if you perform the same experiment again, there is a chance to get a different result, and nature, like throwing dice, draw the experimental results. If it comes to draw the results, it means that every result has a certain probability to be accepted in the experiment. So quantum mechanics deals with predicting the distribution of results.
As physicists have learned, scale size is very important when we examine phenomena in our world. Theories describing phenomena that occur at larger scale in a good way, fall when examining smaller scales, forcing physicists to rethink about the importance of the concept of size.