A twist is a piece of citrus zest used as a cocktail garnish

Cocktail garnish

Cocktail garnishes are decorative ornaments that add character or style to a mixed drink, most notably to cocktails.A large variety of cocktail garnishes are used. Many rum-based cocktails, especially those with fruit flavors, tend to be decorated with tropical-themed garnishes or slices of fruit....

, generally for decoration and to add flavor when added to a mixed drink.
There are a variety of ways of making and using twists. Twists are typically cut from a whole fresh fruit with a small kitchen knife immediately prior to serving, although a peeler, citrus zesters, or other utensil may be used. A curled shape may come from cutting the wedge into a spiral, winding it around a straw or other object, or as a byproduct of the cutting.

The name may refer to the shape of the garnish, which is typically curled or twisted longitudinally, or else to the act of twisting the garnish to release fruit oils that infuse the drink. Other techniques include running the twist along the rim of the glass, and "flaming" the twist.

They are generally about 2 inches long (although length varies), and thin.

Cocktail

Cocktail

A cocktail is an alcoholic mixed drink that contains two or more ingredients—at least one of the ingredients must be a spirit.Cocktails were originally a mixture of spirits, sugar, water, and bitters. The word has come to mean almost any mixed drink that contains alcohol...

s featuring a twist include Horse's Neck

Horse's Neck

A Horse's Neck is an American cocktail recognized by the IBA. It is made with brandy and ginger ale, with a long spiral of lemon peel draped over the edge of an old fashioned or highball glass...

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