The women wear long formals and short formals. It isn't like a set thing, just where what you would to prom or a formal business dinner for women. Men wear tuxes(if they want to spend that kind of money, they are available for rent on the boat) and just dress pants with ties. hope this helps!
I've seen both long and short dresses, from semi-formail cocktail type dresses all the way to beads and sequins. I personally love dressing up so I always wear full-length gowns, but you can go either way and look fine.
Last year we took cruises on Celebrity's Mercury & Carnival's Inspiration. On Celebrity, there were at least 30% long gowns and tuxes, and many short formal dresses (sequins, etc.). Men who didn't wear tuxes wore dark suits/white shirts/club ties. On Carnival (July) we only spotted about 10% tuxes, and about 20% long gowns. Lots of formal pantsuits, lots of sequin-dressy short cocktail dresses, and the rest very nice business dresses. Women wore a lot of black, like black crepe pants w/two different tops for the two nights. There were a few men who just had nice sports jackets & ties. Whatever you decide, you will want to have something special to wear. You have an opportunity to have formal pictures taken on formal nights in front of various backdrops, so can get a studio-style portrait to remember the cruise.