An Alvanian beehive was a nest made and occupied by Alvanian bees. Activity around such beehives was known for being extremely energetic.
In 2373, Quark expected business at his bar to become busier than an Alvanian beehive after Bajor joined the Federation. He expected to do five times the volume of root beer sales alone. Sadly, his expectations were never met as the Bajorans delayed joining the Federation that year. (DS9: "Rapture")