Dictionary Definition:

“A reaction in which one species is oxidized and another reduced; the action or process of this; oxidation and reduction.”

Selected from OxfordDictionaries.com

Functional Definition: 

Oxidation-reduction reactions involve the movement of electrons from one molecule to another. When a molecule is oxidized it loses electrons and when a molecule is reduced it gains electrons. The reason that we say a molecule is reducing with the gain of electrons is because electrons are negatively charged and adding more electrons reduces the overall charge of the molecule they move to.

Sometimes you’ll hear something refereed to as an oxidizing agent, this means that the molecule is being reduced by oxidizing another molecule. Similarly you may hear something refereed to as a reducing agent, this means the molecule is being oxidized by reducing another molecule.

The figure bellow shows two example oxidation-reduction reactions. In the first reaction a hydrogen atom is added and the double bonds shift positions, overall there is a gain of electrons. In the second example the creation of the coenzyme NADH is shown by an overall gain of two electrons.

Figure courtesy of Angel Harraez of Wikipedia Commons