A sweet fizzy Earth drink that Quark stocked for Starfleet customers, which he and Garak used as an uneasy metaphor for the Federation in The Way of the Warrior.
Root beer is a traditional human soft drink, and Quark keeps it in his bar because the Starfleet officers on the station order it. He personally finds it revolting.
Its best-known appearance is in the Deep Space Nine episode The Way of the Warrior. With a Klingon fleet menacing the station, Quark persuades Garak to try a glass. Garak pronounces it vile, and Quark agrees that it is cloying, bubbly and happy, just like the Federation. He adds that if you drink enough of it you begin to like it, which is what makes it insidious.
The two outsiders then admit, reluctantly, that the Federation is probably their best hope of surviving what is coming. Nog, by contrast, comes to enjoy the drink openly.