Pant suits and semi-formal to formal dresses are appropriate for women. Some ships also have theme nights such as Country and Western or Caribbean night. You can dress up or just watch the fun. Dress on board during the day is casual and relaxed. One rule to remember is no shorts are allowed in the dining room for dinner.
Shorts are fine for breakfast and lunch in the dining room.
For cruises to northern climates, be sure to bring warm dry clothing. Good rainwear is highly recommended. While you are in port, the casino and shipboard shops will be closed. All other activities and dining options will still be available. You can come and go as you please, the ship is your own floating resort.