Energy is a scalar property of physical systems, measured in units with dimensions M⋅L2⋅T-2. Energy occurs in several forms; these are potential energy, kinetic energy, electromagnetic radiation, and, according to Einstein's special relativity, mass-energy. Some forms of kinetic energy (such as thermal energy) are often treated separately, because of the historic circumstances of their discovery, and for convenience. One fundamental law of physics is that energy is conserved - it can change in form, but the total energy of a closed system cannot change, and the energy coming into an open system must equal the energy leaving the system.
The dimensions of energy correspond to the application of a force over a distance. Potential energy represents the potential for this to occur, as in the potential of an object to fall in a gravitational field, where the potential is for the force of gravity to be applied to the object over the distance which in can fall. Kinetic energy is the energy of motion, and is equal to ½mv², where m is the mass of the object, and v is the velocity. Special relativity shows that mass can be converted to energy, and that the energy of mass at rest is equal to mc², where c is the speed of light. Special relativity also shows that kinetic energy increases with velocity faster than predicted by Newtonian physics; that additional energy increment is considered to increase the mass of the moving object, as described by the Lorentz equations.
Electromagnetic radiation is also a form of energy ... (There needs to be more here, but I'm running out of steam to write this section.)