Disney ships have a main dining area which features a unique rotational dining system. Basically, each evening both passengers and their personal wait staff rotate to one of the three main restaurants onboard. Each has a different theme, such as Lumiere's which is styled after Beauty and the Beast, or Animator's Palate, where you'll be treated to a fun show during dinner.
Along with the main restaurants, Disney ships also have an adult-only restaurant onboard so you can get away from the kids and have some time alone. Stop by either Palo or Remy for a romantic dinner in a relaxed, elegant atmosphere.
There are also casual dining options on Disney ships where you can grab a quick bite, and throughout the ships you'll also find quick service dining such as Pinocchio's Pizzeria, Flo's Café, and Pluto's Dog House.