Dining times are usually categorize as early, first or main, late or second, and anytime dining, freestyle or as you wish. There are other names, but basically the same idea. If you choose early or late dining, you will have a set time for dining each night and an assigned table. Early dining generally starts anytime from 5:30 to 6:30. Late dining generally starts anytime from 8:00 to 8:30. Anytime dining, Freestyle or otherwise indicated would mean that you do not have a set time for dining and you can come and go as you please. Sometime you have to make reservations in advance, other times you just go and wait for a table. Many cruise lines that offer this flexible dining schedule will require that you prepay for gratuities. Some will add the cost of the gratuities automatically to your cruise total, while others will simply charge you onboard.
When you book your reservation, if your requested dining time is not available, you can request that it be waitlisted. If you are booking far enough in advance, waitlist requests can many times be accommodated. However, sometimes you will be assigned to the time you originally book. Once onboard, if you need to change your dining arrangements, there is usually a place where you can do so. On Disney's Magic and Wonder, this is in Rockin Bar D or Wavebands. The dining room staff usually has some flexibility with this.
Many cruise lines will not accept a request for main dining based on certain medical conditions and you will still have to be waitlisted if not available. This includes diabetes. The idea behind this is that there are so many other dining options onboard, you do not require to eat at the early time.
The choice of early, late or my time dining is really a personal decision. Usually when you have an assigned dining time, you will be seated with other (though you can request to dine alone). You will have the same servers each night. They get a chance to know you and what you like to eat and drink. You interact more with the staff in this set up. With the anytime dining, you won't likely get the same servers each time and you will likely dining with just your immediate party. I have done both and prefer the set dining time, even though I'm not thrilled with the times.
Should you pick early or late dining? This also depends on you and your family. I prefer late dining because sometimes I don't want to go to the shows and just want to relax at the pool or take my time getting ready after getting back onboard from a port of call. Especially in the Mediterranean this was important as many times we didn't get back until just before our late dining time.
For those with small children, you should decide if having the kids awake in the dining room or through the shows. If the shows are more important to you, you may want to go to late dining so that the kids can see the shows. If having family time at the dining table is more important, early dining might be the better choice for you.
This is further complicated on the new Disney ships. The theater does not hold enough guests for half of the guests to go to each show so they will have three shows. With early dining you can choose to go to the show before or after your dinner. With late dining, you will have to choose between two times prior to dinner. This is an assigned time so you will have to go to the show at the time same each night of the cruise.
If something is going on and you just can't make it to your assigned dining time, there is no need to worry. There are usually a few other dining options for you. Many times the main buffet restaurant will offer dinner selections. There also may be a pizza or burger option onboard. There is also usually room service.