Energy is our way for accounting for things in Physics. There are two main types: 'kinetic' which is the energy a body possesses by virtue of its motion, and 'potential' due to where that body is positioned in a field.
The work done on an object by an applied force is equal to the force multiplied by the distance moved in the direction of the force. But sometimes the force is applied at an angle so this must be taken into consideration as well.
The kinetic energy of an object is the energy it posses by virtue of its motion. In this video (with a little bit of stop frame animation) I also go through the derivation and where there is a v squared term in the equation.
Gravitational potential energy is the energy an object has due to its position in a gravitational field, so it depends on the mass, the height and also the gravitational field strength 'g'.
Conservation of Energy
Energy cannot be created or destroyed, just transferred to other forms.
Conservation of Mechanical Energy
Energy cannot be created or destroyed - just transferred from one form to another. This is really useful when we consider the change from KE to PE or PE to KE.
This is how we define power, as well as a couple of simple examples using the formula P = W/t.
The rate of energy transfer is sometimes more useful to consider than the total energy transferred. Not only is P = E/t but it can also be written as P = Fv.
Although we often assume 100% of the energy is transferred from one form to another this is not always the case. When energy is lost from the system (perhaps as thermal energy) then its efficiency decreases.