Caption: Shown is the only physics formula everyone knows: E=mc**2, where E is energy, m is mass and the vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s =3*10**5 km/s ≅ 1 ft/ns.

E=mc**2 is, of course, a basic result of special relativity (1905) and is obtained in the physicsy derivation of special relativity from the special relativity postulates. A physicsy derivation is one where you start with basic axioms, but introduce extra ones as you go along as seems reasonable to physical intuition (i.e., educated guessing) or by clairvoyance (i.e., you believe you know where you have to arrive). Pure mathematics it isn't.

In fact, the derivation of E=mc**2 is remarkably simple though well beyond the scope of this figure.

But what does E=mc**2 mean?

Actually, E=mc**2 means two things:

Meaning 1 of E=mc²:
1. All energy has mass: i.e., exerts a gravitational field and has a resistance to acceleration.
2. The amount of mass is given by m=E/c**2. So E=mc**2 fundamentally means that energy and mass are two aspects of the same thing.
3. To emphasize this sameness, one often uses the unified term mass-energy in relativity speak rather than either of energy or mass. In fact, in the appropriate contexts, mass-energy, energy, and mass are all synonyms. However, one often uses energy or mass depending on which aspect of mass-energy is being emphasized.
4. As an example of Meaning 1, if you add/subtract kinetic energy or heat energy ΔE to/from a system, you add/subtract mass ΔE/c**2 to/from the system.
  Such changes in mass are NOT noticed in everyday life NOR were they observed experimentally prior to the advent of special relativity in 1905 (when people started looking for them) because ΔE/c**2 is usually so small compared to a system's rest mass (see the Meaning 2 of E=mc**2 below). Nowadays, they have been super well verified at least by indirect means.
Some further points:
1. The physical laws of conservation of mass and conservation of energy were viable as separate physical laws in 19th century because the minute changes mass caused by changes kinetic energy, heat energy, and other forms of energy (i.e., force field energies) were below detection then.
  In modern formulation, the laws of conservation of mass and conservation of energy are fundamentally the same thing and are considered as separate laws only as emergent laws in cases where changes in rest mass are below notice (see the Meaning 2 of E=mc**2 below and Wikipedia: Relativistic mechanics: Rest mass and relativistic mass). However, it many applications scientific and technological, those changes are below notice.
2. Note there is NO system with overall negative mass, but negative mass contributions exist since there are negative energies. If you add up all the energy of a system, it will be positive and divided by c**2 will be the total mass of the system.
  Actually, yours truly believes that a measurement of mass of an object is the only direct measurement of energy and it is only a measurement of total energy. All other energy measurements are indirect measurements since you measure some other quantities and calculate energy from a formula. For example, kinetic energy KE=(1/2)mv**2 (the energy of motion in the classical limit) is measured by measuring m and v and using the just given formula.
3. Re kinetic energy. Say an object is moving at velocity v with respect to you. It has kinetic energy KE=(1/2)mv**2. But this means that its mass has increased in your reference frame though NOT in its own reference frame. In this case, the increase in mass of the object (relative to you) requires a special formula for its determination since the kinetic energy formula KE=(1/2)mv**2 is only the classical limit formula and KE/c**2 is only a semi classical physics formula. The exact formula is simple:
  m(v)=m_0/sqrt[1-(v/c)**2] ,
  where m_0 is the rest mass (see the Meaning 2 of E=mc**2 below and Wikipedia: Relativistic mechanics: Rest mass and relativistic mass). Note E=m(v)c**2 is still correct for m(v).
  Since kinetic energy changes with reference frame, you may wonder is gravity a reference-frame dependent quantity. In the classical limit, NO because in the classical limit we simply do NOT consider changes in mass given by the semi classical physics formula KE/c**2: they are deemed negligible.
  When NOT in the classical limit, general relativity (1915) tells you how to calculate gravity effects in general and yours truly thinks the issue of gravity as reference-frame dependent quantity becomes a bit unmeaningful.????
4. There is a very tricky point that must be mentioned. The conservation of energy principle does NOT necessarily hold absolutely according to general relativity (1915). In fact, it does NOT seem to hold for observable universe as whole. But all is NOT lost. General relativity gives us the general-relativity energy-momentum conservation equation (see also Car-120) as an absolute physical law to which the conservation of energy principle is just an emergent principle applying on scales much less than the whole observable universe. The conservation of energy principle may also NOT hold exactly for gravitational waves, but this is NOT certain (see Roger Penrose, The Road to Reality, 2004, p. 467--468).
Meaning 2 of E=mc²:
There is such a thing as rest mass energy (usually just called just rest mass for simplicity) since massive particles have intrinsic mass NOT due to any other energy form.
This is the energy calculated from E=mc**2 for an object of mass m when the object is at rest in an inertial frame: hence the name rest mass.
Since any energy form can be converted into other all other energy forms, rest mass can be converted into all other energy forms. But note conversions are NOT always easy to do in practice.
Some further points:
1. The term massive particles means particles with rest mass. The most common massive particles are the particles that make up ordinary matter: i.e., electrons, protons, and neutrons. In astro jargon, we refer to ordinary matter as baryonic matter.
  Exotic dark matter particles (if they actually exist) also have rest mass and are massive particles, but they are NOT baryonic matter.
  To emphasize, massive particles can be observed when at rest.
2. Mass is sometimes referred to as quantity of matter. This definition is exactly meaningful if you change "mass" to "rest mass in protons, neutrons, electrons, dark matter particles (whatever they are), etc." since massive particles are considered to be matter as opposed to massless particles (see below) which are NOT considered to be matter. Note in astrophysics, ORDINARY matter consisting of protons, neutrons, and electrons is called baryonic matter as opposed to dark matter (consisting of dark matter particles whatever they are).
  Note that objects including composite particles (e.g., atoms and molecules) that are at rest on some observed scale have contributions to their mass from many kinds of microscopic scale energy. Are those contributions part of the rest mass of the objects? Yes or no depending on what you mean with the meaning usually determined by context.
3. As we discussed above in Meaning 1 of E=mc**2, when you give massive particles more kinetic energy (in some local inertial frame) by accelerating them, you give them more mass (in that local inertial frame). In fact, their mass goes to infinity as you accelerate them to the vacuum light speed. This follows, in fact, from the relativistic formula for the mass of a moving object with rest mass:
  m(v)=m_0/sqrt[1-(v/c)**2] ,
  where m_0 is the rest mass. Since giving massive particles infinite mass is giving them infinite energy by E=mc**2, special relativity dictates that you CANNOT accelerate massive particles to the vacuum light speed. This conclusion is experimentally verified so far by particle accelerators among other ways. The conclusion is also consistent with the statement that the vacuum light speed is the fastest physical speed since formula for m(v) seems meaningless for v/c > 1.
4. There are also massless particles (photons, gluons, and the hypothetical gravitons) which have NO rest mass.
  Note that massless particles always move at vacuum light speed c = 2.99792458*10**8 m/s (exact by definition) ≅ 3*10**8 m/s =3*10**5 km/s ≅ 1 ft/ns relative to any local inertial frame, and so are NEVER at rest in a local inertial frame. But could they still have rest mass in some sense? NO. If they had rest mass, then the formula
  m(v)=m_0/sqrt[1-(v/c)**2] ,
  would dictate that they have infinite mass-energy since they are moving at vacuum light speed and they do NOT have infinite mass-energy.
  But E=mc**2 means that massless particles do have mass since they have energy (finite energy). To be super precise, rest-massless particles should be called rest-massless particles, but that's NOT the convention.
5. Actually, there is a lot of rest mass. For example,
  E=mc**2=(1 kg)*(3*10**8 m/s)**2 ≅ 10**17 J = 25 megatons TNT
  in explosive chemical energy (see Wikipedia: TNT equivalent), and so it's a good thing we CANNOT easily convert rest mass into explosive kinetic energy given the human propensity for making bombs. For example, see the figure below (local link / general link: explosion_1954_bikini.html).
6. In fact, there is NO practical way of just converting the rest mass of macroscopic lumps of matter entirely into other forms of energy.
  But it can be done in principle. For example, just rapidly collide 0.5 kg of matter with 0.5 kg of antimatter and both will annihilate to form gamma rays (and maybe other stuff ???) which will give explosive heating with the above calculated amount of 25 megatons TNT. But there is NO practical way to accumulate any macroscopic amounts of antimatter.
  Creating even large microscopic amounts of antimatter is challenging in the lab.
  At the microscopic level, the mutual annihilation of matter and antimatter goes on all the time at a very low level including wherever you are. For example, positrons (the antiparticles of electrons) are products of certain radioactive decay processes (specifically some beta decay processes) that occur at a low level just about everywhere. But the rate of positron production is very low usually. The produced positrons run into electrons pretty quickly and mutually annihilate to create gamma rays. The rate of heating from this natural and common process is relatively low.
7. What of using rest mass for commercial power? For example consider converting 1 kg of rest mass per second to electric power:
  P = mc**2/t=(1 kg)*(3*10**8 m/s)**2/(1 s) ≅ 10**17 W = 10**5 terawatts
  which is a lot of terawatts relative to societal needs since world commercial power usage is currently ∼ 20 terawatts (see Wikipedia: World energy supply and consumption: Primary energy production (2021); see also Physics file: energy_units.html). Our energy resources would be endless if we could easily convert rest mass into other forms of energy.
  Ever since the advent of special relativity in 1905, people have been mesmerized by how much energy is available in principle in rest mass. But the practical ways of getting a significant fraction of it from matter are limited to nuclear reactors and nuclear bombs (see the figure below: local link / general link: explosion_1954_bikini.html).