The unit of E (energy) is the Joule.
A Joule is defined in units of kilogram times meters squared per seconds squared.
This doesn't come from Einstein, it comes from the vis-viva equation,(E = 1/2 mv**2) developed by Leibniz in the 17th century for classical physics applications in orbital mechanics.
To put it in plain English, a object of mass m (kilos) traveling at a velocity v (meters per second) has a kinetic energy of E (Joules). Example: a 2 kilogram mass falling at a 3 meters per second has a kinetic energy due to motion of 9 Joules.
Einstein's E = mc**2 for the TOTAL energy inherent in any mass has a square term in it so the Energy term will come out in the right units. Example: a 1 kilogram mass can be converted to 9x10**16 Joules of Energy.
It is merely a mathematical consequence which is inevitable from the derivation of the equation, there is nothing magical about it.
see for yourself
http://www.karlscalculus.org/einstein.html
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