A "full publish" of a site refreshes every page on a site regardless of the last time it was published. Furthermore, full publishing guarantees that the navigation elements are consistent across an entire site.
An "incremental publish" of a site only effects those pages that have updated since the last publishing run.
We offer "on-demand" publishing, commonly referred to as the "Publish Now" feature. Right click on any content item or folder, and you should see the "Publish Now" menu item. If you do not see Publish Now, it means that the item has never entered a publishable state (equivalent to the item being in the Public workflow state).
Publish Now on a folder will trigger a recursive, incremental publish of that folder. Recall that incremental publishing only effects those items which have been changed since the last edition was published.
Publish Now on a content item will publish the last public revision of the item.
We ask that you not abuse the Publish Now feature. Instead, use the Preview menu item if you want to see what a page will look like before you publish it. Repeatedly editing the content item and triggering Publish Now, will only cause needless numbers of revisions of the content item to be stored.
Think of publishing in the CMS as you would with a newspaper. The public does not read the news until the pages are published. The CMS has two types of publishing runs.