The way it was explained to me was that it was a box you can't see into. If you open the box, it lets the cat escape, so observing it directly affects the state of it.
A better example was opening a freezer to see if ice had formed. Doing this in a hot environment prevents ice from forming because it lets a bunch of hot air into the freezer. Looking at the state of ice forming has a direct influence on whether or not ice has formed.
This is somewhat true, but also misleading. The problem lies in the assumption of what variables have "fixed" numbers. On the macro scale, we tend to assume that things like velocity and location are known, deterministic values. In reality, an object is described as a wave function without precise velocity and location, but give an error smaller than we care to observe.
Take, as a grossly simplified example, a sound wave. If you want to make a strongly defined, very sudden pulse, you make a pulse.
The problem is, that as you make that pulse tighter, it becomes harder to break it down into specific frequencies (or pitches). Similarly, you can have a single tone wave that provides well defined frequency:
But the wave must go through at least a full cycle before you are able to discern a single tone. Thus, two things intuitively unconnected, time of pulse and tone, are actually mutually exclusive in their precision. However, no matter what sound you make, there is a very real wave function, even if you can't give an exact time and tone.
So look at the cat again. The mistake is in assuming that being alive or dead is a strictly deterministic state. In reality, the cat's state (at least from the perspective of anyone other than the cat), is matched to the wave function relating to the radioactive decay. The wave function is very much real and determined, but does not give you a precise piece of information on time of death that you assume exists. However, as the half lives pile up, the probability that the cat's state will collapse to dead when you view it will increase infinitely close to 100% certainty with infinite time.