Unlike the random sprig of mint that might show up on a restaurant dessert plate, mint in cocktails actually serves a purpose: It adds delicious herbal yet fresh flavors that provide a nice contrast from the sweet and more bitter flavors in a drink. But just throwing a sprig into your drink doesn't do anything — you've got to smack it first!
If you've ever watched a bartender make a classic mojito, he muddles — or gently presses a muddler or spoon against — the mint leaves first. This helps to extract the oils where all the mint flavor is locked up and gives the mojito its trademark flavor and aroma.
But if the mint isn't going to be muddled or chopped up into a cocktail, how do you extract that flavor? Just tossing it in there won't do anything, so that's where your hands come in. Place the leaves or sprig in one hand and gently smack it with the other — this warms up the mint slightly and starts to extract the oils before you use it to garnish your drink.
And to be honest, it's a pretty slick professional bartending move if you're trying to impress your guests. Smack away!