Entropy is a concept in thermodynamics. It measures heat loss. When any process happens in a physical system, energy is dissipated. When you drive a car, the engine doesn't just produce forward motion, but also noise and heat. This noise and heat is useless energy that creates disorder, rather than order.
The Second Law of thermodynamics says, as Flanders and Swann put it, "Heat won't pass from a cooler to a hotter. You can try it if you like, but you far better notta,". Another way of putting this is that entropy will always increase.
Heat, you see, is the disordered random movement of particles. And in any closed system, randomness will always increase and order will decrease. As a simple example, if you get a tray full of marbles, half black and half white, and shake it about, they will mix up in a random fashion. It is extremely unlikely that they will separate into white and black, unless some outside force separates them.
Any action you take to create order in some area - like sorting the marbles into white and black must destroy order somewhere else (the movements of your arms in moving the marbles create heat, and ripple the air molecules, and require energy from your body that requires respiration, and so forth). The disorder created must always be greater than the amount of order created. Imposition of order leads to escalation of disorder. (Anyone thinking of cybernetics now, and Ashby's Law of Requisite Variety, which states you can't control something unless you have more options available to you than there are variables, is thinking along the right lines. Incidentally, a friend had a wonderful application of this to Mister Miracle, when we were discussing comics...).
Now this is *the* fundamental law in physics - and indeed in science generally. A theory can contradict anything else in science and it'll be given a fair hearing, but the second law of thermodynamics is inviolable no matter how good your hypothesis is, if it contradicts the second law, it's wrong (with some minor exceptions in the quantum realm, which probably aren't really exceptions anyway).
And the consequences of this law are simple. Heat and energy will eventually spread across the whole universe, in absolutely equal amounts, all completely unusable. The universe will end, not with a bang, but not even with a whimper. It will simply be a placid sea of utterly random particles, moving very slightly, almost imperceptibly, forever, with no pattern or form.
But here's where we get to the really interesting bit, from my point of view at least:
Entropy and information are the same thing.
Entropy is disorder, remember? And information is the same thing as unpredictability. Mathematically, the amount of information contained in an information source is *identical* to entropy. In other words, entropy is *the same thing* as the amount of information needed to describe a system. The more information you need to describe the system, the more disordered the system is.
This means that any operation on information is an operation on entropy. And entropy *cannot* decrease. This is, believe it or not, why your laptop gets so hot, when you'd think that since it has no moving parts the heat it generated would be minimal. Anything that is processing information, by definition, *has* to increase the total amount of entropy in the universe, in this case by generating heat. More generally, the more precisely we can describe any one part of a system, the less precisely we can know what's going on anywhere else (the simillarity of this to Heisenberg's Uncertainty Principle only just occurred to me as I was typing the previous sentence, so I can't comment further if this is a simillarity that everyone has noticed already or if it's a new insight - anyone else know?)
Every thought you have, every piece of information you learn, every time you put two and two together to make four, you are increasing the order of your brain at the expense of the order of the universe.
If this post has made you think at all, then by doing so you're contributing to the heat death of the universe. I hope you're all pleased with yourselves, you bunch of vandals.