Depending on the length of your cruise vacation, you will have at least 1-2 evenings that are designated as formal nights. Your pre-departure cruise documents will tell you exactly how many formal nights there will be, as well as which specific nights they will be, so you can be sure to be prepared.
Now, many cruise passengers have mixed feelings about getting all dressed up on formal night-some like it and some don't-but the important thing to remember is that formal cruise wear evenings are always optional. Most major cruise ships today offer a host of 24-7 casual dining establishments that are always available for all those "anti-formal night" passengers.
If you wish to dine in the main dining room (s) however, formal attire is required. So what is considered cruise formal wear? You will find that people will have varying opinions as to what should be considered formal, but typically cruise formal wear is anything that you would wear to a wedding or any fine dining restaurant.
Most men opt to wear either a tuxedo or nice dark suit and tie. Tuxedo rentals are available aboard most cruise ships. Women will generally wear anything from a simple cocktail dress, to an elaborate, glittering ball gown. The degree to which you choose to dress on formal nights is entirely up to day. Again, it's whatever you feel most comfortable wearing.
Many cruise ships may also have at least one "themed" night, especially on longer itineraries, where you will dress according to a certain theme. Again, participation in these special nights is entirely voluntary, and your cruise documents will specify which evenings are designated as themed. So get all dolled up, go out, and have a good time. It'll be like your prom night all over again!