You asked Daniel to give you an answer but if you do not mind I'll offer my view also, that way you can compare it with those of Daniel and others.

Seems to me that you understand the math part thoroughly, but according to RL (the local physics god;-) you must understand how the formula was derived.

In order to understand how the formula came into being, one must understand the words used to describe the characters or symbols, that is where the understanding of the language comes in.

Since your question was brief, I'll try to be brief with my answer. I'll start from the very beginning and explain the meaning of the important words first.

Jumala = God = Creator

taivaan (taivas) = heaven = Space = Force = potential for motion = potential for energy = cubic area that does not contain any kinetic energy.
I will refer to this fundamental constituent of the universe as 'potential force', and represent it with the letter u.
The numeric value of 'u' can be calculated by using the formula u=cm2.
Potential force u = constant times mass squared.

maan (maa) = earth = mass = m = that which can move and change in density = the force responsible for kinetic enegy. I will refer to this fundamental structural constituent by the name kinetic force and in the mathematical formula it will be represented by the letter k. The letter k, has the same numeric value as mass or m. k=m

Valkeus (valo) = light = constant = c = that which can move (vibrate) at a very high rate per unit of time.

Valo or c has a numeric value of 2.9792458*108m/sec.

The mass (ordinary matter) that we are familiar with is a combination of potential force u and kinetic force k, or in mathematical terms, u/k. If ordinary matter is accelerated to the value of c then the result is the maximum amount of 'kinetic energy' that the quantity of mass can exert.

You said:

On the face of it, it looks like you have an area (square meters) undergoing an acceleration, like that of gravity- 10m/s2?

You are right, the square measure comes from the internal structure of matter. That force is a fundamental part of the way mass (k) interacts with space (u).

An isolated unit of fundamental mass (k) would have the area 4 pi r 2 and a volume 4 pi r 3/3 at any instant of time.

The formula for energy then becomes, E=(u/k)c or E=mc2

Both formulas give the same results.

There is far more to the understanding of the structure of mass and the forces involved, but this short explanation is a good starting point in my opinion.

Johannes