We know that strange things happen when objects move relative to other objects. Clocks run more slowly, lengths get shorter, and mass increases for the moving object, relative to an observer at rest. These are well confirmed over the last century from countless experiments. We also know E = mc^2 comes from special relativity. But how did Einstein do it? Where did he get the idea that energy and matter aren't just related, but actually equivalent to each other?
Check this out!! It is one way of thinking about it, and getting to a result that shows energy and matter are of the form E = mc^2. It makes use of the binomial approximation when thinking in terms of everyday speeds, which are far slower than light.