That one is apparently what happens in a nuclear reaction of the atom bomb kind. The tremendous power of the bomb is due to conversion of a small amount of mass into a lot of energy. That's what they say, anyway.
As far as basic units are concerned, force is thought of as a product of the mass and the rate of change of the speed of the object. And then speed is a product of space and time. We're not real clear on what time might be, and why it is considered a dimension like height, width, and depth. It gets worse. We say space is 3-dimensional, but it is treated as 4-dimensional when they consider time, and now physicists are thinking in terms of more dimensions, 11 maybe. I don't know, I'm still open to suggestion.
That is the usual explanation, but that is not quite what Einstein's equation implies. Any change in the energy of a system -- whether it be the result of a nuclear reactions, a chemical reaction, or a cooling breeze -- causes the mass of the system to change. Increase the energy, you increase the mass; decrease the energy, and you decrease the mass. It has nothing to do with nuclear reactions.
Mass is not converted to energy in an atom explosion; it might be more accurate to say that as the energy leaves the system, it carries mass with it.
As far as basic units are concerned, force is thought of as a product of the mass and the rate of change of the speed of the object. And then speed is a product of space and time. We're not real clear on what time might be, and why it is considered a dimension like height, width, and depth. It gets worse. We say space is 3-dimensional, but it is treated as 4-dimensional when they consider time, and now physicists are thinking in terms of more dimensions, 11 maybe. I don't know, I'm still open to suggestion.
Two points here:
1. Force is a derived unit in the SI units; however, in the so-called "English Engineering" system, force is a fundamental quantity. As a result, we end up using "pounds" to refer both to force (lbf) and to mass (lbm). (I prefer SI units.)
2. It seems to me that time is taken as a fundamental dimension because it is a basic or axiomatic concept. It is hard for me to imagine explaining time in terms of something simpler. (But like you, I'm still open to suggestion.)