They can add more meat to the bones of Nate’s relationships, as well as giving you more information about the area you’re in. There are 36 all together, some of them resulting in additions to your journal that don’t actually count as journal entries, yet are still entered in the journal.
The optional conversations are a new addition to Uncharted (and, if we’re to believe that there won’t be an Uncharted 5, we won’t be seeing them again).