The effect of Bitters in a drink is to balance, round out and complex the flavor. Your mouth has taste receptors for sour, sweet, and salty; AND it has a receptor for bitter. The more receptors triggered as a drink tickles on the way down, the more interesting the drink. You know you have used Bitters correctly when the person enjoying the drink says, "Wow, there is something going on in the background of that drink". Consider that a slam-dunk.
Why in the world would anyone want to put something called "Bitters" into a drink? In fact, Bitters are critical in the best drinks. The first publication of a bartenders' guide which included cocktail recipes was in 1862 - How to Mix Drinks; The Bon Vivant's Companion, by "Professor" Jerry Thomas. In addition to recipes for Punches, Sours, Slings, and the like, were 10 recipes for drinks called "Cocktails".
A key ingredient which differentiated cocktails from other drinks was the use of Bitters.
