A ballroom was a large spacious room where people could dance. It usually has a type of flooring with attributes suitable for dance, with said floor being called a "Dance floor".
In 2152, Captain Jonathan Archer told Hoshi Sato that her quarters aboard Enterprise NX-01 would feel like a ballroom in comparison to the cramped catwalk they were sheltering in. (ENT: "The Catwalk")
In 2365, Geordi La Forge described his idea of where Worf's tenth anniversary of his Klingon Rite of Ascension would take place and what it would look like: "Twenty piece orchestra, magnificent ballroom, everybody in formal wear." Wesley Crusher then corrected him, explaining the painstik-ridden gauntlet Worf would have to endure. (TNG: "The Icarus Factor")