Basically, it manifests the relationship between the coefficients and roots of a polynomial. Consider a quadratic equation $$$ax^2 + bx + c$$$. Lets suppose that $$$\alpha$$$ and $$$\beta$$$ are the roots of this equation, then:

$$$\alpha + \beta$$$ = $$$-b / a$$$

$$$\alpha \beta$$$ = $$$c / a$$$

I am pretty sure that you are familiar with this relationship without knowing the fact that it is called the "Vieta's formula"