A ball is a formal dance.
Attenders wear evening attire, which is specified on the invitation as black tie or white tie (the most formal). Social dance forms a large part of the evening; actual ballroom dancing may or may not occur.
The word ‘ball’ is derived from the Latin word “ballare”, meaning ‘to dance’; the term also derived into “bailar”, which is the Spanish and Portuguese word for dance (verb). In Catalan it is the same word, ‘ball’, for the dance event. Similarly, in Scottish Gaelic, the word “ball”, is a noun meaning ‘a dance; a spot, a place.’