What do Oxidation numbers tell you?
Oxidation numbers provide information about the ability of an element (or compound) to lose or gain electrons during a chemical reaction.
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.
Here is a great YouTube video on oxidation numbers:
Oxidation number tells you the possible properties of the constituent element.
Some elements are more reactive in certain oxidation state than the other states.
For e.g. Cr(VI) can oxidize compounds while Cr(III) cannot oxidize.