What is the practical implementation of mass-energy equivalence?

It is the equation of energy
It is the relationship between energy (e), mass (m) and the speed of light (c) squared. Basically it says that energy and mass are part of the same thing, as related by the quation. It means it is possible to convert mass into energy and energy into mass.
Short explanation: energy = mass x (speed of light)^2
Long explanation:
This is stating that energy equals mass times a constant (the speed of light squared which equals approximately (299 792 458 m/s) squared).
So basically the idea is that energy (heat, movement, etc) can be converted into mass, and the difference grows less the faster you go. Therefore meaning the more energy you have the more mass you have. This explains why you cannot go faster than the speed of light, because you'd end up with (approaching) infinite mass and would therefore need infinite energy.
E = m*c^2 is Einstein's famous equation relating energy (E), mass (m), and the speed of light (c, for celeritas, Latin for "speed").
For example, the Sun fuses hydrogen (H) atoms into helium (he). It takes 4 H atoms to make 1 He atom. However, when you add the mass of 4 H, you get a tiny bit more than the mass of one He.
The difference is tiny, but with the large number of atoms involved in the Sun's core, it adds up: The Sun loses over 4 million tonnes of mass every second.
The definition of a Watt is "a kilogram metre-squared by second-cubed" or, in math terms: 1 W = 1 kg m^2 / s^3.
That's where the last factor comes from. Simply applying a definition to make the units come out right.
Similarly, if you want to create matter out of energy (you have E, you want to create m), then you use the same equation to find out how much energy is needed to create some specific particle.

E = m*c^2 is Einstein's famous equation relating energy (E), mass (m), and the speed of light (c, for celeritas, Latin for "speed").

In some high energy reactions, such as nuclear reactions and matter-antimatter annihilation, mass is destroyed. If you know how much mass is destroyed, this equation tells you how much energy is created.

For example, when an electron and positron meet (they are antiparticles of each other), they both cease to exist, and two photons are produced. The photons have no mass, but the electron and positron each had a mass, so some mass has been lost. Applying Einstein's equation tells you the total energy of the photons. You simply insert the total mass that was lost into "m", then multiply by the square of the speed of ligh