If you've made edits and saved them, they will not show up on the live site until you also PUBLISH.

This is true of both edits to CONTENT and edits to NAVIGATION.

It's easy to reorder pages in the Pages bar. You just grab and drag. But if you do not open that page and select the Publish or Save & Publish button, the navigational scheme will only change in draft and will not change on the live site.