Each page in the index (and this goes for all indexes, not just clustered indexes) has, as part of the page header, the page number of the next and previous page in the index.

If you ever read the 'chose your own adventure' books, each story fragment in them has a next page to go to. You can kinda think of an index working that way. Read this page, then go to page 75 and read that, then to page 21 and read that.

If an index has no fragmentation, then logical and physical order match, and the 'next page' will always have a higher page ID than the current page.