The terms oxidation and reduction refer to how much oxygen is in the kiln's atmosphere while the kiln is firing. An oxidation atmosphere has plenty of oxygen for the fuel to burn. A reduction atmosphere occurs when the amount of available oxygen is reduced (In a controlled fashion)

Basics of Reduction 

Fire requires oxygen to burn. When there is a lack of oxygen, the fuel does not burn completely and the kiln atmosphere becomes filled with free carbon. The free carbon atoms will aggressively grab up any oxygen atoms they can find. In fact, carbon atoms are so oxygen-hungry that they are able to break molecular bonds. The carbon literally robs the clay and glaze materials of their oxygen. Fuel fired kilns including gas and wood are examples of kilns that can fire in reduction

Basics of Oxidation 

When heated sufficiently, many substances oxidize if there is free oxygen available. Volatile portions of compounds and molecules break free and the free oxygen then can attach to the remaining material, forming oxides. This process is called oxidation. In firing a pottery kiln, the materials will normally convert to their oxide forms. For example, when copper carbonate is fired, the carbon will detach and burn off. As soon as the copper-carbon bond is broken, available oxygen will rush in and attach to the copper, forming copper oxide resulting in a green to black color.

 Neutral Atmospheres

 When a kiln is not in reduction, and there is enough oxygen for efficient fuel consumption but not an abundance of oxygen, the kiln can be considered to be in a neutral atmosphere. Electric kiln firings are generally considered to have either a neutral or slightly oxidizing atmosphere. Many potters question if there is any such thing as a truly neutral atmosphere. Their main point is that there is enough oxygen in the kiln so that the glaze and clay body materials do oxidize.

Results

When the carbon reduces the amount of oxygen in the clay and glaze molecules, the colors and textures of the clays and glazes can change. These changes can sometimes be quite dramatic. For example, glazes with a high iron content may be rather stiff at cone 9 in an oxidation atmosphere, and quite fluid and runny at cone 9 in a reduction atmosphere. Small amounts of iron would be brown or tan in oxidation but blue or green in reduction. Glazes with small or large amounts of copper oxides would fire green in an oxidation or neutral atmosphere but red to violet in a reduction atmosphere, thus the term copper red