Every night we have dinner on the weeks that I have my kids we discuss a specific topic.  We don't watch TV or anything brain killing like that.  A few days ago my oldest boy Anthony asked me just what e=mc2 really meant.  Since that's such a misunderstood term by the general pubic I had to ask him " are you talking about time travel or the geometry of the universe?".  Of course he said time travel. 

Since it took me a little time to explain to him I figured I'd share this with everyone.  I'll break it down for you in 2 ways… the kid friendly explanation and a more scientific explanation.

Kid Friendly version:

In Einstein's famous Theory of (Special) Relativity, he laid down two basic concepts:

The laws of physics are the same in all reference frames.   This means that they're all the same no matter when or where.

The speed of light through a vacuum (like outer space) is the same and the person watching you will see what everyone else watching you will see.

These concepts basically say that if you were moving through space with a constant speed and in a constant direction, the rate at which you would travel forward in time changes a little.  The idea it that the faster you travel through space, the slower you travel through time.   It's not the same as time travel but it tries to explain how time can be ' changed ' for the person watching you.

In a nutshell it means that speed effects mass and this effect can be seen by anyone watching you, it also effects length as well. The faster you travel through space, the more massive you become and the thinner you become in the direction of your going. When they say time slows down for you according to people watching you it means your mass increases, and that your width changes.  This means that anyone watching you would see these effects.  To you, you're not moving and you measure your time, your mass, and your width as you always did, it should be just what you expect to see as if you weren't moving at all.   The main difference is for someone not moving along with you, they would see your clock, heart beat, etc. run slower than expected.  They would see your mass seem to increase.  If the person watching you were to push you, you wouldn't accelerate as much as they'd expect.  They would see your width in the direction of your motion as thinner.

As much as I can type this in layman's terms, the concepts are hard to understand if you can't imagine you standing still while the world speeds by around you.  Given enough speed you would seem to travel through time. 

Ok the big boy explanation, This took a lot more time to chart out.

Einstein's theory says that the direction of light spread (propagation) should be changed based on gravitational forces (gravitational fields), this is totally different than what Newton predicted. Sciencitific observations seem to show that Einstein is right, both about the effect and its size.

It's important to note that Einstein's theory discusses Special Relativity which is more in line with General Relativity and not Specific Relativity.  That's a whole different set of theories that have been somewhat altered by Einstein's, now accepted theories.

The General Theory of Relativity predicts that light traveling in a vacuum (like outer space) and coming from a strong gravitational force should have its wavelength shifted to larger values (also called "red shift"), again contrary to Newton's theory. Once again, observations indicate such a (red) shift, and that its magnitude is correctly given by Einstein's theory.
The electromagnetic field can have waves in it that carry energy we call light. Likewise, the gravitational field can have waves that carry energy and are called gravitational waves. These may be thought of as ripples in the curvature of spacetime that travel at the speed of light.

The real variable here is the make up or geometry of the Universe.  Since space itself is curved, there are three general possibilities for the geometry of the Universe. Each of these possibilities is tied intimately to the amount of mass (the total strength of gravitation) in the Universe, and each implies a different past and future for the Universe:

If space has negative curvature, there is insufficient mass to cause the expansion of the Universe to stop. The Universe in that case has no bounds, and will expand forever. This is termed an open universe.

If space has no curvature (it is flat), there is exactly enough mass to cause the expansion to stop, but only after an infinite amount of time. Thus, the Universe has no bounds in that case and will also expand forever, but with the rate of expansion gradually approaching zero after an infinite amount of time. This is termed a flat universe or a Euclidian universe (because the usual geometry of non-curved surfaces that we learn in high school is called Euclidian geometry).

If space has positive curvature, there is more than enough mass to stop the present expansion of the Universe. The Universe in this case is not infinite, but it has no end (just as the area on the surface of a sphere is not infinite but there is no point on the sphere that could be called the "end"). The expansion will eventually stop and turn into a contraction. Thus, at some point in the future the galaxies will stop receding from each other and begin approaching each other as the Universe collapses on itself. This is called a closed universe.

Just as accelerating charges can emit electromagnetic waves, accelerating masses can emit gravitational waves. However gravitational waves are almost impossible to detect because they're so very weak and no conclusive evidence has yet been reported for their direct observation. They have been observed indirectly in the binary pulsar. Because the arrival time of pulses from the pulsar can be measured very precisely, it can be determined that the period of the binary system is gradually decreasing. It is found that the rate of period change (about 75 millionths of a second each year) is what would be expected for energy being lost to gravitational radiation, as predicted by the Theory of General Relativity.
Today the best of generally accepted theories on gravitation is the General Theory of Relativity. However, only if velocities are comparable to that of light, or gravitational fields are much larger than those encountered on the Earth, do the Relativity theory and Newton's theories differ.

So in a final analysis
In a very careful analysis of exactly what time meant in a system that moves at speeds comparable with the speed of light, Einstein's theory showed that this principle of relativity still applied and that if a body emits energy in the form of radiation then its mass must be reduced by a proportional amount.   This is what the famous equation E=mc² means.

Now you got it ?