This is a cut and paste from the FAQ thread in this forum. It has more info than you asked, but it may help:
Let's preface this by saying that Disney doesn't enforce the dress code in any of the main dining rooms. Having said that, they could choose to at anytime, and guests should be respectful of the dress codes. If you don't want to dress for dinner there are several other casual dining options. Formal wear is available to rent before you cruise, also.
In the main dining rooms most nights are cruise casual. Cruise casual means no shorts, tank tops or swimsuits. Disney used to request no jeans in the dining room. That's not in their official description of cruise casual on Disneycruise.com, but you will still see that request from time to time. In general for men a collared shirt and khaki pants are great. For women there's a broader range, but they should probably avoid casual shorts and jeans. For kids most anything goes, but they should avoid swim suits and casual shorts.
There are a few exceptions to cruise casual. They are listed below.
Pirate Night occurs on all length cruises. The dress for pirate night is pirate attire. It's one of those times that ripped jean shorts will work fine if it's part of pirate attire. Of course if you don't feel like dressing like a pirate, cruise casual works too.
Dress Up Night is for cruises of 3, 4, and 5 nights. Dress up night is not as dressy as the formal nights below, but Disney requests a jacket for men and dress or pantsuit for women. You will see some people very dressed up.
Semi Formal Night occurs on cruises of 7 nights or longer. On some very long cruises Disney adds in a second Semi Formal Night. Semi Formal wear is defined as a suit/jacket for men and a dress or pantsuit for women.
Formal Night occurs on cruises of 7 nights or longer. Formal wear for men is defined as a tuxedo or suit. For women it's a gown or dress.
Palo is the adult only restaurant located on all ships. The dress code is enforced and you will be asked to go change if you do not follow it. The dress code for dinner at Palo is dress pants and a dress shirt or jacket for men. For women it's a dress or pantsuit. They request no jeans, shorts, capri pants, flip flops or tennis shoes.
Remy is another adult only restaurant located on the Dream and Fantasy. The dress code is also enforced at Remy. At Remy a tuxedo or dress jacket is required with dress pants for men. Ties are optional. For women a cocktail dress, pant/suit or skirt/blouse is required for women. They also require no jeans, shorts, capri pants, flip flops or tennis shoes.