Traditional dining - you go to dinner at a set time every night, you sit at the same table with the same people and have the same waiter, your meals are all bought out at the same time, you eat at the same pace as the rest of your table. Some cruise lines physically shut the door so if you are more than 15mins late you are not allowed in.
Anytime dining - you go to eat when you want to between 6 and 9:30 approx, ask to sit with as many people as you wish, eat at your pace. You can read the daily schedule so you can time your dinner to make the shows.
I know which one I prefer...