There will be one required dance your freshman year and one required dance your sophomore year -- I say "required" because you will be required to appear and attend for a certain amount of time.
Ring Dance occurs Junior year (was held last Friday night) -- and is much more fun than the first two.
The freshman event occurs sometime after Parents' Weekend -- I don't recall the timing of the Sophomore event, although I seem to remember that it may also have been in the fall. These kinds of dances are traditional events at military academies -- probably a hold over from the days before females were admitted as cadets/midshipmen. In those days, young women were brought in from nearby colleges -- so everyone had someone to dance with. Today they are seen as chances for young men and women to learn how to conduct themselves at "formal" events and how to "mingle" with officers -- something that you will have to know how to do in the military. They are probably also supposed to be "fun" and a break for the cadets.