You don't need need sophisticated mathematics to understand the basic concepts of Quantum Mechanics.
Consider gravity. How can it be visualized? We can enjoy the parabolic trajectory of a football - and subsequent acrobatic catch; we can anticipate with horrid certainty the crash of the dropped cup, and feel comforted by the fact that the trajectories of the planets follow relatively safe orbits that are based on these same laws. The fact that all matter seems to obey simple equations of motion (forgetting about special and general relativity for now) gives us confidence in our paradigm. The basis of our understanding of gravity is not so much in picturing the object called gravity, but in the effects caused by gravity.
Based on our overwhelming experience that objects effect each other through direct contact, its natural to ask how two bodies can interact at a distance. And this is where imagery helps us to build a deeper understanding. There are several equally good ways to picture gravity, and they are of the same value only if they correctly predict observations. Such images, however, are only constructs that help us picture the phenomena in terms of everyday analogs.
The concept behind the Schrodinger cat is based on events that are rarely, if ever, directly observed in our lives.
For example, space (more accurately space-time) can be pictured as a fabric that is deformed in the presence of a mass. When someone sits next to you on the bed, they make a depression in the mattress to which you are attracted. Is space time really a fabric? It depends on what you mean by a fabric. If its something made of a material or something that you see, then it's not. Its only a construct, which makes it simpler to picture the effect and often simplifies the mathematics. The picture is most useful when it leads to the prediction of new phenomena or helps explain subtle observations. This is not, however, a proof that the image "really" corresponds to reality.
Unlike the "picture" of gravity, the problem with the Schrodinger cat is that the concept is based on events that are rarely, if ever, directly observed in our lives. Getting a deeper understanding of quantum mechanics in general, and the Schrodinger cat in particular, will therefore take a bit more effort.
Once as a teaching assistant in graduate school, I found it impossible to explain a concept. In frustration, I said, "Don't worry about it. Nobody ever really understands anything, they just get used to it." In retrospect, I have found this to
be true. You feel comfortable with gravity because it has always been your steadfast companion. So, the concept of gravity as a real thing is easy to accept.
The Schrodinger cat is a paradox that was introduced to emphasize the weirdness of quantum mechanics. In the microscopic world, it is possible to prepare matter to be in what is called a superposition of states. An electron can be spinning with is north pole facing both up and down at the same time. In the Copenhagen interpretation, once the spin is measured, it can only be found to be in a state of north pointing up or north pointing down. The act of performing the measurement causes the system to collapse into only one of the two states.
Schrodinger proposed an experiment with a cat in a box with a vial of poison that was had a 50 percent chance of being released during the experiment. If the box were designed to be isolated from the environment, the Copenhagen interpretation would say that the cat was half dead and half alive. The act of opening the lid of the box to observe the state of the cat would cause its wavefunction to collapse so that it was either dead or alive. This brought home the very strange notion that, first, the cat was in the weird state of being half and alive at the same time; and secondly, the act of observing the cat either killed it or made it live.
To understand the experiment, we first need to talk about the meaning of measurement. A good example is temperature, which is a quantity that describes the average energy per molecule due to the motion of the molecules in a material. To measure the temperature of a cup of boiling water, one starts with a thermometer at room temperature. Consequently, the thermometer gets hotter and the water cools a bit so the temperature we read is lower than the actually temperature. If the cup of water is small, the measurement has a large influence. You can imagine how complex this simple problem becomes if you try to measure the temperature of just a few molecules! The lesson is that small systems are difficult to measure with an apparatus that affects the system.
In addition, we know from direct observation that particles behave as waves. When a beam of electrons, atoms, or molecules are launched through a small pinhole in a wall and observed on a screen, the particles are observed to bunch up so that they hit only certain parts of the screen. For a circular hole, this results in a bulls-eye pattern of hits. The smaller the hole, the larger the spread in the pattern. You can observe the same effect in a water wave passing thorough a canal that empties into a larger body of water. The longer the wavelength (distance between peaks) the more spreading you see. The reason we don't see these wavelike effects in every-day matter such as a car or baseball is that the wavelength gets smaller as the mass gets larger. (The wavelength of a particle is determined by the pattern of "ripples" observed on the screen).