An intuitive understanding of heapsort?

Question

At school we are currently learning sorting algorithms in Java and I got for my homework the Heap Sort. I did my reading, I tried to find out as much as I could, but it seems I

Answer 1

Suppose you have a special data structure (called a heap) which allows you to store a list of numbers and lets you retrieve and remove the smallest one in O(lg n) time.

Do you see how this leads to a very simple sorting algorithm?

The hard part (it's actually not that hard) is implementing the heap.