Why does the oxidation of organic compounds by molecular oxygen (to produce CO2 and water) release free energy?

Free energy refers to the amount of energy available for use. Oxidation is when the carbon atoms gain bonds to oxygen, as is mentioned in this example. It can also refer to any reaction that moves electrons. Oxidation is literally the gain of oxygen, which increases the positive charge on an atom. Increased positive charges would increase the amount of free energy, or energy that is available and not tied up.

This is the opposite of reduction, which is the loss of oxygen. Both actions, oxidation and reduction, together are called a redox reaction.