Briefly, remembering that since about 1880 or so it has become
increasingly impossible to really discuss details of anything in
physics in English or other language without benefit of mathematics,
what the equation says is that matter and energy are two forms of the
same thing and that you convert between the two by either multiplying
or dividing by the speed of light squared.
But this conversion is just like converting between inches and
centimeters, it isn’t an explanation, it is just a number.
The equation says nothing in particular about time or the speed of
conversion, in fact, although time is a component of speed, this
equation squares speed and time squared is meaningless, at least in
this context.
See
http://www.madsci.org/posts/archives/sep2001/1000903792.Ph.r.html
This irreverent look at the question actually offers a pretty good explanation:
http://www.stresscure.com/hrn/einstein.html
How he came up with the equation is relatively simple, so to speak. He
saw that an easy way to explain some experimental results by others
was to assume that the speed of light was constant.
By using the speed of light as a constant in some earlier equations of
physics, one result that popped out was that e=mc*2 which surprised a
lot of people, including Einstein. The equation says nothing about how
to convert either direction, it just provides an equation for
determining the magnitude of the conversion.