A dance in which two dancers move in triple time as they turn together in circles is called a waltz, and it's also the name of music that's written for that sort of dance. If you aspire to be a competitive ballroom dancer, you'll need to master the waltz.
Waltz is also a verb, so couples may waltz around the ballroom while the band plays a waltz. When you waltz, you face your dance partner with one hand on their waist or shoulder and the other clasping their hand. The two of you move in a gliding spin. It its earliest days, the waltz was considered a bit shocking—previous dances were "open," with couples side by side, rather than "closed," with dancers facing each other.