The oxidation state, often called the oxidation number, is an indicator of the degree of oxidation (loss of electrons) of an atom in a chemical compound.
Conceptually, the oxidation state, which may be positive, negative or zero, is the hypothetical charge that an atom would have if all bonds to atoms of different elements were 100% ionic, with no covalent component.
In chemistry, the terms oxidation and reduction refer to reactions in which an atom (or group of atoms) loses or gains electrons, respectively.
Oxidation numbers are numbers assigned to atoms (or groups of atoms) that help chemists keep track of how many electrons are available for transfer and whether given reactants are oxidized or reduced in a reaction.
The process of assigning oxidation numbers to atoms can range from remarkably simple to somewhat complex, based on the charge of the atoms and the chemical composition of the molecules they are a part of. To complicate matters, some atoms can have more than one oxidation number.
Luckily, the assignment of oxidation numbers is governed by well-defined, easy-to follow rules, though knowledge of basic chemistry and algebra will make navigation of these rules much easier.