[SmG Altair]

I'll explain resonance with an example. A double bond is made up of two electron pairs. So, there's a total of four electrons making up that bond. Two of these electrons shift to one of the atoms forming that bond. This gives the latter a negative charge because it's now accommodating more electrons than it can. Now in some cases it starts a chain shifting of electrons, simply because these atoms can't accommodate the extra electrons. This phenomenon is mostly seen in covalent compounds with multiple bond and is called resonance.

Now, why do they shift like that? The answer to this is fascinating. Everything in nature is trying to attain stability. Likewise, these covalent compounds are trying to attain stability. By temporarily shifting the electron pair, the compound makes more and more resonance structures*. By attaining different forms and interchanging between them, the compound attains stability. This is why a compound is more stable when it has more resonance structures. 


*Remember if a compound undergoes resonance then it will have at least two resonance structures 


Now, what's formula charge? Let's look at what Wikipedia says :

In chemistry, a formal charge is the charge assigned to an atom in a molecule, assuming that electrons in all chemical bonds are shared equally between atoms, regardless of relative electronegativity.

Assuming that electrons in all chemical bonds are shared equally between the atoms. When a compound undergoes resonance electrons migrate (temporarily), then they wouldn't be shared equally. So, resonance has to be explained using formula charges.