The well-known equation, is a shorthand version of Einstein's full equation:
Where m is the particle's mass, p is the particle's momentum, and c is the speed of light.
The equation states that the total energy of a particle has two contributions that add in quadrature: one from the particle's mass (mc2), the other from the particle's motion (pc).
If a particle is not moving (or is moving very slowly compared to the speed of light), the equation reduces to the familiar shorthand version. When a particle is accelerated to near the speed of light, the p2c2 term makes a significant contribution to the particle energy.
This is how high-energy collisions of light particles in a particle accelerator can create much heavier particles. For example, the LHC will accelerate protons to 0.999999991 times the speed of light. Traveling at this speed, a proton has a total energy of 7 TeV, while a proton sitting still has an energy of 0.938 GeV.