What changes, and what doesn't
Only the order. The pages are copied into a new document unchanged, so text stays selectable, images keep their resolution and the file size stays about the same. Page numbers printed on the pages are part of the content, so they will not renumber themselves.
Moving many pages at once
For heavy rearranging, it is often quicker to combine tools: pull out the pages you want with Extract Pages, remove the ones you don't with Delete Pages, or join several files with Merge PDF and reorder the result here.