Do you understand what a heap is and how it can be represented by an array?
The idea of heapsort is that in a heap, it is easy to find the greatest element (it's on top). It's also quite easy to form a heap from a set of numbers. It's really just much more intelligent version of selection sort.
What is the problem with being "in place"? Many algorithms are in-place. For example bubble sort is. A naive version of quicksort isn't, as you'd create arrays "less than pivot" and "more than pivot". Quicksort can be made in-place too though. Of course all algorithms use some extra space for variables. That space is negligible when sorting a large array though.
I believe, by additional storage space, he means additional "array spaces" or arrays. The videos I gave you work fine on showing the "in place" part: you only have to keep track of the number of elements sorted so far.