The Special Theory of Relativity was proposed in 1905 by Albert Einstein (1879-1955). The reason it is "special" is because it is part of, or a "special case" of, the more comprehensive and complex General Theory of Relativity. The latter, General Theory, was proposed by Einstein in 1915.

Albert Einstein (1879 - 1955)

Space and Time.
In an everyday co-ordinate system, such as a map, it's possible to specify a location using just dimensional distances. For example, to someone looking for buried treasure we could say "go east for 20 miles, north for 5 miles, then dig down 30 feet". We have just specified a three dimensional co-ordinate system. To this, Einstein added another factor, that of time. This still makes sense in our everyday world: "go east for 20 miles, north for 5 miles, dig down 30 feet, and then wait until 3 o'clock when I will meet you to share the treasure!". However, if we go at very high speeds, speeds close to the speed of light, things begin to change in a very strange way. The faster we go the more our clock slows down relative to someone standing still; time, for anything moving, changes! Instead of space and time being separate things they are the same thing, called space-time. In short: "moving clocks run slow".

Einstein's Two Postulates.
The theory is based on two principles (postulates):
Physical laws are the same in all frames of reference. That is; any event within a portion of space (a frame) can be specified by three spatial dimensions (east-west, north-south, up-down) and one temporal dimension (time). Also, the laws that apply to us in everyday circumstances (Newton's laws) also apply within each frame of reference.
The speed of light is constant. By this it is meant that in a vacuum, such as in space, the speed of light is always the same, regardless of the speed of someone observing it.
The first postulate is seemingly simple and trivial. If I sit and wait an hour in New York, an hour passes. If I sit and wait an hour in Edinburgh then an hour also passes. I am, almost exactly, in the same bit of space (frame of reference), moving around the Sun at the same speed wherever I sit on the Earth. The way time passes in all frames of reference is governed by the same laws.
While the first postulate is pretty much what one might expect the second requires a little more explanation. The speed of light is very close to 300,000 kilometres per second (around 186,300 miles per second). Everyday experience tells us that if a bus is moving north at 30 miles per hour and we are also walking north at 5 miles per hour then the bus is moving away from us at 25 miles per hour:

But what if we move in the same direction as a light beam? Let's say we produce a pulse of light into space by quickly flashing a torch (flashlight) on and off. We then follow the beam of light in a very fast rocket moving at 100,000 km per second. How fast is the light beam moving away from us? Common sense tells us that it is moving away from us 300,000 km minus 100,000 km per second. In other words, the light beam is 200,000 km per second faster than us. Wrong! Remember that the speed of light is always the same regardless of our own speed. From our rocket we would see that the beam of light is still moving away from us at 300,000 km per second! Likewise, if we were moving towards the beam at a very high speed we would still see the light coming at us at 300,000 km per second! This has enormous implications!

Time dilation.
If the speed of light stays the same then what is going on? Something else has to change. That "something" is time.
As odd as it seems time is not constant. More accurately, space-time is not constant. It can be changed, bent and twisted. The faster we go the more time slows down ("moving clocks run slow"). This is only noticeable, normally, at very high speeds such as those approaching the speed of light, 300,000 km per second, which is approximately 7 times around the Earth in a second.
What does all this mean? One of the most dramatic consequences of this is that time itself will run at different speeds for two people moving at different speeds relative to each other (hence "relativity"). Let's have an example. Keith, a 30 year old NASA astronaut, blasts off from Cape Canaveral in his very high speed rocket in the year 2010 on a 10 year mission to a nearby star. After a short time he is travelling at 270,000 km per second, that is, 90% of the speed of light. To Jeanette everything looks normal in his rocket; the clock seems normal and time passes for him the way it did back on Earth. His identical twin sister, Jeanette, is a NASA ground controller for the mission. Ten years pass on Earth before the rocket returns and when it does something is immediately apparent; while the Earth-bound Jeanette has aged 10 years, her high-flying "twin" brother has only aged 5 years! How can this be? Well, again we are back to "moving clocks run slow". At 90% of the speed of light time slows down to about half of that relative to someone who is stationary. So while 10 years have passed for Jeanette only 5 years have passed for Keith because his "clock" was running at half the speed of those on Earth. This is called the twin paradox. Remember that while Keith has only aged 5 years he still felt that time was passing normally; this is not a way of living longer! Not only was his clock running slow as far as a ground based observer is concerned, but his time was running slow.

How fast can I go?
Some other consequences of the special theory of relativity are that:
Distances shrink in the direction of motion.
Mass (appears to) increase with speed.
Nothing can travel faster than light.
For reasons of brevity the first point will not be covered here and the latter two only very briefly.
Under the "rules" of special relativity the mass of any object appears (to a stationary observer) to increase as the speed of the object increases. At 90% of the speed of light mass will approximately double, but at 99% of the speed of light the mass will increases by about 7 fold. As we get closer to the speed of light the mass increases very dramatically until at the speed of light it would be infinite. The more something weighs the more energy is required to move it, as we know from everyday experience. To move something of infinite mass would require infinite energy and this is clearly not possible, hence nothing can travel faster than light. We live in a universe dominated by Special Relativity where faster than light travel is not possible. There are, however, ways of breaking out of the constraints of the special theory and travelling at speeds far in excess of that of light, at least for tiny particles. As well as being very unusual and beyond the scope of the Special Theory, the conditions for this are, as far as is yet known, of no practical consequence.

Is it real?
This is all well and good, but what evidence is there? After all it's just a "theory". Some clarification is required here. Unlike its use in the everyday world, physicists use the word theory only when there is substantial and verifiable evidence for an observed phenomena. In this sense a scientific theory is quite unlike a conjecture or idea, and more often than not requires a great deal of observational and experimental evidence before attaining the status of theory. In the case of Special Relativity there have been very many experiments carried out and all of them have provided evidence that Special Relativity is correct. These range from experiments involving sub-atomic particles in high speed accelerators to the slight, but expected, different clock rates of some space exploration vehicles (such as the Voyager inter-planetary probes) as compared with those on Earth.
One example of supporting evidence for the theory is a much simpler experiment that was first carried out in 1971 and has been repeated many times since then. Atomic clocks have been carried on aircraft making long flights such as over the Atlantic ocean. An aircraft, even the fastest, goes at a tiny fraction of the speed of light, but at any speed "moving clocks run slow". With an atomic clock on the ground and one in the aircraft it is possible to measure the tiny differences in time produced by moving the clock. At the speed an aircraft travels these differences are measured in millionths of a second, but they are real and in extremely close agreement with what special relativity says they should be. Despite being counter-intuitive the theory has passed every experimental test so far carried out. The chap below would have been quietly pleased:

Albert Einstein

The Full Form of the Equation.
So far we have referred to the energy of very high speeds as "relativistic kinetic energy". This is fine for allowing us to work quickly through the equations and to keep them simple, but there has to be a more formal way of expressing what we mean. As with the term mc2, a detailed derivation of the full equation for E = mc2 is beyond the scope of these pages. However, to those familiar with the basic mathematics of special relativity the way in which we take into account the kinetic energy of E = mc2 will come as no surprise.
For any non-stationary body the total energy is given as:

This equation takes into account the total energy (E), the mass of the body (m), and the speed of the body (v). As such it accounts for both the relativistic mass increase and the relativistic kinetic energy.