alden pretty much nailed it. It is basically tortillas, cheese of your choice and whatever you want to put in it.
My favorite quick and easy is to buy the fully cooked and seasoned grilled chicken breast strips in the freezer section. You can add spinach, squash, tomatoes, green/yellow/orange/red peppers, mushrooms, or whatever you have that needs to be used in the refrigerator. It is all good in a quesadilla.
Plus, you can experiment with various cheeses, grilled veggies, meats/poultry/pork...
It's practically a Barbie Intro to Cooking dish. It's a blank slate for you to express yourself. Your canvas is the tortilla, your basic paint is the cheese, but you take it from there. Minimalist, collage, whatever.
No, it is not a taco if you use just one. You do not grill tacos to melt the cheese.
I love using my double burner grill to make quesadillas. I have the back burner lower to give me time to get new ones started on the portion that is on the front burner.
I bet bananas with some nutella and Camembert or brie cheese would be a good desert quesadilla. Cooked pear or apples slices with a touch of brown sugar, cinnamon, and cheddar would be good too. Many times my mother would serve apple pie slices with cheddar cheese melted on top. It would be similar to that dessert.