Energy is a physics concept that has been around forever. Energy conservation is firmly ingrained in the minds of theorists as the one law which has and will never be broken. This simple concept, however, leads to some pretty cool things to think about if you have the time.
Energy is one of those things you learned about if you took a high school or college physics course. You probably learned about it and found that it made many problems easier to solve, but didn't think much of it. Here's a summary of what your physics teacher mentioned:
When you make an object move by imparting a force onto it, you exert work while the object gains energy. We define the amount of energy the object has as the amount of work you had to exert to get it into the state it is in. For example, if you push a cart down the street, it begins to move and attains velocity. The motion of the cart is a form of energy called kinetic energy.
Another example- When you lift up a bowling ball, you are exerting a force on the ball to counteract the force of gravity. The energy gained by the ball is called gravitational potential energy. It is called 'potential' energy because it has the potential to become something else.
For example, if you were to drop that bowling ball, the ball's gravitational potential energy would be converted into kinetic energy, and it suddenly becomes very simple to calculate how fast the ball is traveling the instant before it hits you in the foot.
What we call "conservation of energy" is the thing that makes the concept of energy so useful. The really cool thing about it, however, is that the whole concept of energy really just came about as a mathematical trick- a mathematical trick that turned out to reveal something incredibly profound (another such example would be of entropy, which was used in thermodynamics as a math trick long before people realized it actually represented a physical quantity). Here's a little bit of background in classical mechanics:
In Newtonian mechanics, everything is derived from four assumptions: Newton's three laws of motion, and Newton's law of gravity. The three laws state that: (1) an object in motion stays in motion unless acted upon by a force, (2) force equals mass times acceleration, and (3) when one object exerts a force on another, the second object exerts an equal force on the first in the opposite direction. Newton's law of gravity just establishes the nature of gravitational forces between two massive objects. These four assumptions are a physicist's dream. They are simple and concise, yet describe a huge mess of observations- including Kepler's laws, which had previously gone unexplained for decades.
So, where in these assumptions does energy come in? The answer is it doesn't- at least not explicitly. There's a whole lot of talk about forces, but nothing about energy. Nothing that is, until someone comes along and shows that you can prove (from Newton's laws) that the total energy in a closed system is always constant (that is, so long as there's no friction). In Newtonian mechanics, the concept of energy is purely optional. In principle, you could use Newton's laws to solve for anything you'd like to without the word 'energy' so much as crossing your mind.
Now, lets return to the bowling ball example we went through before. You may have noticed that I intentionally only took the example through to the point right before the bowling ball lands. So let's ask the obvious question now- What happens to the bowling ball's energy after it lands? I think we're in agreement that the bowling ball stops after landing, so its kinetic energy is gone, and it no longer has the potential energy it has before you drop it. Conservation of energy isn't very useful if chunks of energy can suddenly disappear without explanation.
Well, that question was answered by James Joule, a physicist whose work is so essential that the standard unit of energy is named after him. What Joule did that was so important is he forced water through a perforated tube and observed that the temperature of the water increased. He also did a similar experiment by heating water with an electrical energy source. The conclusion that was reached from these experiments was the fact that heat, which was understood to be a substance that made the temperature of objects rise, was really just another form of energy.
So, the answer to our bowling ball crashing to the floor question is this: The bowling ball heats up the floor. Some of the energy also escapes in the form of sound waves, which eventually dissipate by heating up the walls and other objects they bump into. The important thing to notice is the fact that conservation of energy, which was originally our little mathematical trick, is still true in the face of forces that we didn't really consider in the first place.
These forces I'm referring to are called non-conservative forces and include things like friction and wind resistance. The thing that these forces share is that they all create heat. The reason they're called non-conservative is the fact that once energy is converted into heat, it becomes theoretically impossible to convert all of it back into some other form (this is where entropy comes in). This isn't to say that the energy is not conserved- it is only converted to a form that makes it irretrievable.
Now that we've cleared that up, lets look at the bowling ball example from the other way: Where did the energy that raised the bowling ball come from?
Well, the energy that powers your muscles is released in a chemical reaction that converts ATP into ADP. The energy that was used to create the ATP in the first place comes from chemical reactions that convert the food you eat into waste product. The energy stored in food, if you trace it back, originates from photons that travel from the sun and are absorbed in the leaves of plants. I'm sure you all are familiar with the Calorie and all of its stress-inducing properties. But did you know that the Calorie is really just another unit of energy? You could literally take the caloric content of a jelly donut and calculate how many bowling balls you could lift with the energy it provides.
Now, speaking of photons from the sun- the sun gets its energy from the fusion reaction in its core which continuously converts hydrogen into helium, releasing a lot of energy. This reaction has the effect of heating up the star to high temperatures and photons are emitted through blackbody radiation. Just about all sources of energy we use today originate from this blackbody radiation. The exception comes in if you happen to live in an area which is powered by a nuclear reactor. The energy in that case comes from a nuclear reaction involving radioactive isotopes you can find in the soil of your lawn (albeit in tiny quantities).
If you're being really thorough, you might remind yourself that all the energy that powers the sun, as well as your neighborhood nuclear reactor, was released to the universe in the big bang.
To this day, conservation of energy remains one of the few conservation laws that has not been violated, even in the face of other vast changes to physical law. Take, for example, Einstein's relativity. Changes were made to our understanding of energy that you'd never see coming. Formulas like those for kinetic energy had to be completely changed (the speed of light started showing up everywhere!). It turned out that mass was really another form of energy. Despite these changes (or because of them), the basic tenant that the energy of a system is constant remained intact. So many ideas that were firmly ingrained in our minds regarding things like mass, time, and space were thrown away while energy was one of the few that remained.
So, here's another example of something more modern that would seem very strange in Newton's days. A piece of gamma radiation (which is really just a high-energy photon), if it has enough energy, can interact with a nuclear electric field, disappear, and create an electron-positron pair. The electron goes off and does what an electron does, but the positron, which is basically a positively-charged electron, does something that is truly remarkable. The positron bounces around until it loses its kinetic energy, eventually getting trapped in the electric field of an electron. The two particles then annihilate each other, and in their place two gamma rays are emitted in opposite directions.
Care to guess what the energies of these two gamma rays are? Well, if you recall Einstein's mass-energy relation, E = mc^2, you can calculate the rest energy of both the positron and electron, and it happens to be 511 KeV. The energy of the two gamma rays are, not coincidentally, also 511 KeV. The two gamma rays carry off the energy that was released when the electron and positron disappeared.
The example above illustrates what the world of modern particle physics is like. Particles routinely appear and disappear and do other things you wouldn't imagine is possible. Imagine for a second what the world would be like if two baseballs could collide and both subsequently disappear in a huge flash of light. The laws that govern the things we normally see on a daily basis don't apply at the particle level, yet things still follow the basic tenant of conservation of energy, which we knew from Newton's days and didn't need to exist in the first place. Things didn't need to be that way.
As remarkable as the concept of energy is, one might find that it is also a necessary one. After all, the universe would not have any semblance of order unless there was something that was held constant. That 'something' was something we just happened to call "energy".