Yes teachabcdee, your children will attend formal night, as well. At least my daughters have always wanted to dress up and have a wonderful meal. Now, if your child is "too cool" to go, Camp Carnival, I believe, has a meal that evening. It might be a pizza party or hanging out on the Lido Deck with hamburgers. But, it's casual.
My girls wear skirts and blouses or dresses with sandals. I have seen boys wearing khaki pants (no shorts) polo shirts or button down shirts and a tie, if they like. Some even wear suits and ties, but don't feel that's necessary.
Keep in mind that on the formal nights it's the best way to have a beautiful formal picture taken of your entire family for a fraction of the cost that you would pay for a sitting at a studio at home. That's what our family does at least. Whenever we entertain, people always love to see our new cruise portrait. You can see how much your children have grown through the years with each cruise. (and, unfortunately, how much we've aged)!