What is the process of reduction when referring to metals within the earth?
It appears your question is referring the process of "reduction" as applied to chemical process.
In chemistry the process of reduction is applied in general to any chemical reaction in which molecules of the substance reacting gains electrons. More particularly, this term is applied to the process in which a substance loosed oxygen atoms. In this sense the process of reduction is opposite of the process of oxidation.
The metals as existing in the natural form within the earth are generally in the form of oxides of those metals. For example. iron ore contains iron in the form of FeO and Fe2O3. To obtain the pure metal from their oxides the metals need to be refined. This process of refining includes, among others, the process of reduction to convert the oxides of the metals to the pure metal form.