The term oxidation was originally used to describe reactions in which an element combines with oxygen.
Example: The reaction between magnesium metal and oxygen to form magnesium oxide involves the oxidation of magnesium.
The term reduction comes from the Latin stem meaning "to lead back." Anything that that leads back to magnesium metal therefore involves reduction.
The reaction between magnesium oxide and carbon at 2000C to form magnesium metal and carbon monoxide is an example of the reduction of magnesium oxide to magnesium metal.
After electrons were discovered, chemists became convinced that oxidation-reduction reactions involved the transfer of electrons from one atom to another. From this perspective, the reaction between magnesium and oxygen is written as follows.
2 Mg + O2 
2 [Mg2+][O2-]
In the course of this reaction, each magnesium atom loses two electrons to form an Mg2+ ion.
Mg Mg2+ + 2 e-
And, each O2 molecule gains four electrons to form a pair of O2- ions.
O2 + 4 e- 2 O2-
Because electrons are neither created nor destroyed in a chemical reaction, oxidation and reduction are linked. It is impossible to have one without the other, as shown in the figure below.
