The Law of Conservation of Energy is fundamental to the study of physics, including thermodynamics, mechanics, and electricity. It simply means that energy cannot be created or destroyed. Machines such as boilers, motors, generators, and gasoline engines simply convert energy from one form to another; they do not create energy.
For any closed system, the Law of Conservation of Energy requires the following statement to be true:
ENERGY IN = ENERGY OUT
That is, all of the energy input to a system must eventually leave the system, in the performance of useful work or in the form of waste. Conversely, energy cannot be extracted from a system if it wasn't input to the system first. For example, a motor cannot deliver more mechanical energy than is supplied to it from its electrical source.
Now consider a much larger and more complex system: a coal-fired power plant. All of the energy input to the plant is in the form of chemical energy, which is locked in the molecules of the coal, and must eventually leave the plant. This does not mean that all of the energy in the coal is eventually output by the generator. Only a portion of the coal's energy is converted by the generator because there are many "losses" within the plant. These are places where energy leaves the plant cycle before being converted to electricity in the generator.