As an object falls in free fall, what energy change is taking place?

Before the object begins falling, it has gravitational potential energy which can be calculated by mgh (mass x acceleration due to gravity x height). As it begins falling due to the force of gravity, that gravitational potential energy is converted into kinetic energy, which can be calculated by 1/2mv^2 (1/2 x mass x velocity x velocity). That is the main way that energy is converted in this situation, but some energy is also converted into heat due to fluid friction with the air (commonly called air resistance).  

The Law of Conservation of Energy states that energy can be neither created nor destroyed, only converted from one form to another. In the example of a falling object, the total energy the objects starts with needs to equal the total energy the object ends with. For the sake of learning this concept, let's ignore friction for a bit. The object begins with only potential energy, and the instant before it hits the ground it has only kinetic energy because it has lost all of its height. So, the initial potential energy will equal the kinetic energy of the object right before it hits the ground. The potential energy has been converted into kinetic energy.