Video: As many bartenders know, one of the secrets to a tastier drink is playing with fire. Flaming an orange (or any citrus, really) is an old trick that looks impressive, but why does it work? First off, there's a lot of flavour stored in the peel -- that's the whole reason you order drinks "with a twist". That flavour comes from volatile oils stored in the skin's many pores, among which is limonene. Besides having a strong orange aroma, limonene is a hydrocarbon just like petroleum, making it extremely flammable.
As for the introduction of a miniature fireball, its the same principle as many other foods: caramelisation. Heat is what makes toast better than regular bread (if you disagree, fight me), and what turns a one-note orange flavour into a complex addition to a negroni variant. It will also impress the hell out of your friends.