My husband is on the cruise critic board more than I'm on this one.
http://www.cruisecritic.com Your cruise line may also have a board on their site. Sounds like you booked through Carnival & I know they do.
But, to answer your question, formal night is pretty laid back on Carnival but it will also depend on who you are seated with as to how dressed up some people get. I have heard that the ship out of Galveston allows blue jeans & cowboy hats in the formal dining room (because of some Texans' ideas of formal)
Before I get flamed I would like to point out that I attended a small country church growing up and the men's idea of church clothing was their least faded pair of blue jeans with a shiny belt buckle, western style shirt and to clean off their boots before church so I completely understand and am not offended by this idea of formal. To someone who wears bib overalls 7 days a week--newish blue jeans, western shirt & clean boots is formal.