What does "would substitute all {{subst:templates}} to the editor" mean exactly?
Could you please provide an example?

What does "edit something in the result" mean?

Let's say we have a template {{Hello}} with content "Hello {{{1}}}!".
Then I'm making a page and I write the following:

{{subst:Hello|hdicu}}

Then if I click the button, it would change the text I wrote to:

Hello hdicu!

For example if I wanted to change Hello to Hi without the button, I'd have to either copy contents of Hello template to the editor and replace {{{params}}} with right values or save the page in order to change it.

There is already a "Show Preview" button. Why is yet another button needed?

The button would do the change the wikitext to what it is after saving.

I don't see why MediaWiki should support editing content of some Template page within a completely different page.

I didn't mean that it would change the template itself. I meant that if you want to substitute a template and make a small change to the substituted content.

The button would do the change the wikitext to what it is after saving.

Isn't that what the Preview function in more modern editors, like VisualEditor, would be for?