now I need to think of what it means in the program.

You can't pass arrays to a sub. The only thing that can be passed to a sub is a list of scalars. The solution is to pass references to arrays, references being scalars.

In thinking about this I believe what is happening is like "nesting".

I didn't look at how recursion is used here, but it's usually used to divide and conquer. Let's take merge sort, for example.

Sorting

+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
|   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |   |
+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+---+
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is done by sorting

+---+---+---+---+---+---+---+---+-------------------------------+
|   |   |   |   |   |   |   |   |                               |
+---+---+---+---+---+---+---+---+-------------------------------+
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and

+-------------------------------+---+---+---+---+---+---+---+---+
|                               |   |   |   |   |   |   |   |   |
+-------------------------------+---+---+---+---+---+---+---+---+
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independently then merging the results. How does it sort the two halves? Well by breaking each down into two halves and sorting those. Etc.