I was thinking about the oxidation number system a few days ago when I was helping my son learn long division. Long division is a 'method' that gets you to the correct answer, but it represents a step in learning mathematics, where the operation of solving the problem has almost completely detached from the conceptual underpinnings. You move the decimal point here. You keep your columns straight. You follow the steps, and don't have to really think about what is going on underneath. You get the answer.
Oxidation-reduction is analogous to long division within chemistry, and few students are ever really challenged to see the underpinnings of the system, even though to do so makes redox much more coherent. What, at heart, is going on in a chemical reaction? Defamiliarize your thoughts. Look at it in terms of the barest essentials. On one side of the reaction you have charge densities, nuclei and electrons, in one form, the reagents. On the other side of the reaction, these charge densities are in a different form, the products. As we have discussed, you can imagine the electrostatic potential energy change from reagents to products by imagining pulling apart the reagents and letting them fall together as the products. If the volume and temperature are constant, this electrostatic potential energy change maps directly onto enthalpy change.
If the chemical bonds in the reagents are weak, it does not take a great deal of energy to break them apart, and if the chemical bonds in the products are strong, a great deal of energy is released as the nuclei and electrons fall together into a deep potential energy well. Such a reaction would have large negative enthalpy change. What does this have to do with oxidation-reduction? Oxidation-reduction is a systematic way that chemists have developed, which allows you to easily predict the enthalpy change of the reaction in a simple step like way. When an element with a high reduction potential (high electronegativity) forms a new chemical bond, it pulls the electron density within the bonding orbital inwards towards its electron greedy nucleus. Elements like oxygen or fluorine have a big powerful nucleus shielded by only a thin layer of electrons, so when they form new bonds, there is a potential energy decrease not only because of molecular orbital formation, but also because they are 'siezing electron control', i.e. pulling negative charge inwards. You would have to do a lot of work to get the electrons away from such an element, so very electronegative, high reduction potential elements form strong, low energy bonds. By assigining the elements reduction potentials, and then keeping track of shifts in electron control using the oxidation numbers, oxidation-reduction gives one an easy way to account for the energy changes within a chemical reaction as a narrative of electron control. The oxidation state or oxidation number of an element is a shorthand way of accounting for the shifts (or transfers) of electron density from one atom to another when compounds form. When the electron density is shifted toward the more electronegative element, that atom is said to have control over the electrons in redox terms, and its oxidation number decreases; the element having lost electron control in the compound gets a positive change to oxidation number.