Energy comes in many forms. Any moving object has what physicists call "kinetic energy" due to its motion. This energy depends on the speed of the object, and on its mass. ("Mass" is very similar to, but not exactly the same as, "weight".) An object which is set on a shelf has "gravitational potential energy" because it has the potential (due to gravity) to gain kinetic energy if the shelf is removed, or if the object should fall from the shelf. Heat is also a form of energy, which can ultimately be traced to the kinetic energy of the individual atoms and molecules that make up a substance. And there are many other forms of energy.
The reason that all these phenomena are referred to as energy - the idea that links them - is the law of Conservation of Energy. This says that if we add up the total amount of energy in the universe (we can describe energy quantitatively with units such as Joules or kilowatt-hours), the total amount never changes. In other words, energy is neither created nor lost, even though it may be converted from one form to another. For example, an automobile is a device which converts heat (inside the cylinders in your engine) into kinetic energy (the motion of your car). A light bulb converts electrical energy into light (two more forms of energy).
In his theory of relativity, Einstein discovered another form of energy, sometimes referred to as "rest energy". I've pointed out that a moving object has energy due to its motion. But that same object, Einstein discovered, will have energy even if it's not moving. The amount of rest energy in an object depends on its mass, and is given by:
(As if I was going to finish up these web pages without writing that somewhere!) Because the speed of light is such a big number, the rest energy of a typical object is way bigger than any other type of energy the object might have. But this usually doesn't matter because in everyday life the rest energy of an object just stays rest energy, and isn't converted into some other form that would allow us to notice it, such as heat or kinetic energy. Relatively small amounts of rest energy are converted into other forms in nuclear power plants, nuclear weapons, the sun, and a few other places, but by and large, rest energy is generally unnoticed.
The sum of the kinetic and rest energy of an object can also be written mathematically fairly easily,
Notice, that at everyday speeds, gamma is approximately 1, so the sum of the rest energy and kinetic energy is approximately the same as just the rest energy. In other words, at everyday speeds the rest energy of an object is much much greater than its kinetic energy. However, at speeds very close to the speed of light, gamma can become much larger than 1, and the kinetic energy of an object can become much larger than its rest energy. (The rest energy depends only on the mass of an object and not on whether it's moving or not.) This is very important for physicists that work with particle accelerators, such as the ones at Fermilab near Chicago, and CERN on the French-Swiss border. This is also important to us if we wish to consider how fast an object can travel.