To quote Serious Eats:
Celery bitters might sound like something that hipster mixologists invented while turning everything edible into a flavor of bitters, but cocktail curmudgeons can rest easy knowing that these bitters were actually around in the 1800s. Celery bitters went out of style around Prohibition and didn't come back until just a few years ago. A few drops of this savory and unusual concoction can completely change a classic cocktail—and inspire tons of new recipes.
Serious Eats also has a great recipe to make your own, or you can pick up a small bottle to add a little umami and spice to your cocktails.