before we get to the more fancy implications involved in q.m. (like Schrödinger's cat), i'd like to bring out one of the basic things, and why we even have quantum mechanics.
one of the most important things to keep in mind is that a light can behave like a beam of particles, and particles can behave like waves. all of this has been experimentally verified, and classical mechanics cannot provide an explanation.
the thing with the Schrödinger's cat is that it implies that by observing/detecting/measuring something we are, in fact, changing the thing/process in some essential way. the cat ''experiment'' was devised as a thought experiment to illustrate the Copenhagen interpretation.
essentially, when we want to learn about something unknown to us, upon doing our measurements we are changing the very thing we want to study (it is said that the wave function collapses upon measurement). in the cat thought experiment this means that in the box, the cat is both dead and alive, and it is only when we open the box to look (or try to obtain the value through other measurements) that the reality materializes. (bear in mind that a cat is a macroscopic entity and this ''experiment'' cannot be devised on any cat. cat is supposed to represent microscopic elements (like an electron) to which quantum mechanics applies).
this was also revealed when they shot electrons at a screen that had slits in it (the double slit experiments). they shot one electron at the screen at a time. the amazing result was an interference pattern! this implies that one electron somehow went through both slits at the same time and interacted with itself to create an interference pattern! (Feynman) (this is AMAZING! truly one of the most fascinating things ever discovered). this could only happen if the electron is a wave and not a particle, like we're used to thinking.
they then added a detector to determine through which one of the slits the particle actually went through. but, now the interference pattern vanished! electron went through one of the slits, and one only, and behaved like expected of a particle. the measurement changed the outcome.
so, in conclusion, light (energy, wave) can sometimes behave like it's particles, and the reverse is true – particles can sometimes behave like waves (
all matter exhibits both wave and particle properties). and that human measurement changes the result. this is true in case of the microscopic scales of the universe, to which quantum mechanics applies.
P.S. one of the most fascinating implications in quantum mechanics is that every electron (or any other microscopic particle) in the universe appears to ''know'' what all the other electrons are doing at all times.
P.P.S. even something as simple as a proton, for example, does not have a stable inner structure. in fact, its inner structure is in constant change and much more complex than three quarks.
(i just wanted to mention these two, as they are incredible mind-expanding realizations).
-------------------------------
recommended reading:
[COLOR="DeepSkyBlue"]
Don Lincoln -- Understanding the Universe from Quarks to the Cosmos
Brian Greene -- The Elegant Universe[/COLOR]