Funny enough, i see it in a lot of drink recipes...even i have included it in the negroni recipe on this page. Yet most people do not know exactly how to "express an orange peel" and after searching for it online, it's not really explained too much online.
 
Expressing an orange peel means to bring the oils on an orange peel to the surface of the orange skin. This can be done simply by removing the skin of an orange with a paring knife or a vegetable peeler...then twist/flex the skin of the orange to bring out the oils.
Be sure not to take too much of the white parts under the peel. That brings a lot of bitterness to the cocktail if you drop the expressed peel into your drink.
Simply fold the peel along the curvature of the stripe and pinch or gently twist to release the oils. The oils will spray along the fold, so aim it over your drink.
Another popular method is called flaming an orange peel. This is done by bringing the oils of the orange skin to the surface by gently warming it with a lighter.
_Wave a lighter or match flame under the orange peel to bring the oil to the surface. There should be visible oil. When you are ready, squeeze the peel (in the same fashion as the expressing an orange peel) at the flame and it should ignite. Not only does it look cool, it does bring a bit of extra flavor into your drink. Just remember to aim the flame at your glass and you are good to go. 
 
 
__Even with equal parts Campari, gin, and sweet vermouth, the bitterness of a Negroni firmly establishes the drink as a Campari-based cocktail. No one is undecided about a Negroni. This Italian big brother to the Americano and distant cousin to the martini is so bitter that its dissenters swear it should be stored in the medicine chest. Its fanatical adherents bask in its ruddy glow and tongue-tingling taste. Some contend that this classic cocktail dates back to Florence in the 1920s, when the flamboyant count—and noted tippler—Camillo Negroni asked for a splash of gin added to his Americano. Others say that the drink, mixed with vodka or gin, has been around as long as the Americano. The Campari company, itself unsure of the origin, eventually decided that the drink should be called a Negroni to avoid confusion with all the other Campari cocktails.

For a longer drink, serve a Negroni with a splash of soda. The cocktail may also be shaken and poured straight up in a cocktail glass.
_
INGREDIENTS:
1 ounce gin
1 ounce sweet vermouth
1 ounce Campari
Slice of orange

INSTRUCTIONS:
  1. In a mixing glass, pour the gin, Campari and vermouth.
  2. Add ice. Stir along the outter edge 7 times, then strain into a cocktail glass.
  3. Express the orange peel over the glass and drop it in.