They let a single page use a different navigation menu than the rest of the site. Default Header / Default Footer means the page uses the standard site navigation. Choosing one of your Menu Groups (created under Menu Groups / Menu Builder) makes that group's links appear as the header or footer on this page only.

Saving the page records the assignment; the same assignment can also be made from the Menu Builder's Show on pages box. Changing the page slug later keeps the assignment (menu links are updated automatically).