Antonio said:
According to Art, "ball" is a noun [C] for a large, formal occasion where people dance. What type of dance are we talking about, for a formal occasion? Can you please, give me some examples to understand the use of the word "ball" in this particular definition?
Antonio, I agreee with Art on that definition of a ball. From my experience, usage of the word "ball" is reserved for very extravagant affairs. For example: Cinderella went to a ball at a castle where there was much fanfare and royalty present.
Generally, you need to be invited or buy an expensive ticket in order to attend one. Of course someone could organize a small dance and advertise it as a ball just for the fun of it, but that would be the exception, not the rule.
The only ball I have ever been to was a Mardi Gras ball. It was required that the men wore tuxedos and that the women wore formal evening gowns. These balls are structured affairs where the schedule of events follows a strict tradition of pomp and circumstance. They are usually held in a large municipal auditorium, and in New Orleans, many are held in the Super Dome. The one I went to started out with a formal presentation of the krewe's royalty and officers.
Krewe = the mardi gras organization. ex: Krewe of Rex, Krewe of Bacchus, etc. This was followed by the presentation of elaborate short plays/skits. The majority of the ball-goers like me just sat in the audience enjoying the show being put on by the actual krewe members. After the skits were over, we all remained seated while the king and queen had the first dance. They were then joined by the lesser royalty and officers. Finally, the royal subjects (us in the audience) were invited to join them. Shortly after, food and alcohol was made available and it turned into a giant party with multiple live bands, etc., and over the course of the evening, much of the formality was given over to debauchery.

The important things to note are the formality in dress and protocol which are inherent at a ball. The rest was for your entertainment.
Bambino