The Equation Everyone Knows

Most physics students are aware of Einstein's famous equation,

E = mc²

This equation is often seen on T shirts carrying an image of Einstein.  It is used to name office buildings to highlight the innovative work being carried out inside. In many ways this equation is the public image of relativity. But what does this equation actually mean? Even among physicists, this equation, often called one of the most important equations of the twentieth century, is often misunderstood.