I know that the Voyager and Explorer are larger, 7-day cruise ships, which means that they do have a formal night (sometimes two, so bring two formal outfits). They normally call the initial formal night "Captain's Dinner", although you don't actually dine with the Captain. This night usually comes with a before dinner or after dinner reception (depending on what time you eat), which includes free cocktails and hor'deveures.
Besides eating in the dining rooms every day, you always have the option of eating in the cafe (buffet style), or since you are going on a larger, more elaborate ship, you also have he option of eating in the restaurant (Johnny Rockets or Portofino's for example). Be Warned: You WILL have to pay for these meals, as they do not come along with the price of your cruise as the cafe and dining room does.
If you purchase alcohol off of the ship, they will require to hold it until you reach homeport, and you will receive it back once you debark.
NOTE: I have sailed on RCCL before, and I know that the smaller ships such as the Sovereign Class and Vision classes do not have the extra restaurants on them; only the Voyager class ships. Nevertheless, i enjoyed the dining room and cafes on the various classes. The food in my opinion was excellent, and everyone in my travel group (from ages 3-67!!!) enjoyed everything we ate.
Hope this helps, and i hope that you have an AWESOME time! I'm sure you will, as long as you keep realistic expectations.