It's a phrase used to ask about the types of breakfasts someone has. It's like asking "What do you eat for breakfast?" or "What kind of breakfasts do you like?"
Here are some examples:
* "Que desayunos?" (What breakfasts?)
* "Que desayunos te gustan?" (What breakfasts do you like?)
* "Que desayunos hay?" (What breakfasts are there?)