Delicacy is just a fancy way of talking about foods that some people think are really special or luxurious. Imagine if there was a dessert that was made with fancy ingredients like gold leaf or rare fruits. Some people might think that dessert is a delicacy because it's not something you can get just anywhere.
People might also call certain foods delicacies if they are hard to get or they are made in a special way. For example, people might say that caviar is a delicacy because it comes from expensive fish and not everyone can afford it. Or, they might say that a particular type of cheese is a delicacy because it's made in a certain way and only a few people know how to make it.
Basically, delicacy just means that some people think a certain type of food is really special or fancy. It's like when you get a really cool toy and you think it's the best thing ever, except with food!