Published - viewable by the general public.
Unpublished - hidden from view, only site administrators can see.
All new content on your website is automatically set to 'Published'. That way you don't have to worry about what happens when you add something - it goes where it's supposed to and is seen by who it's supposed to be seen! However, sometimes it's useful to unpublish an existing page or to set a new page as unpublished if it's a work in progress.
If you are editing or adding a page, the option is in the same exact place. Scroll down to the bottom and click 'Publishing options' to expand the menu. You'll notice that 'Published' is already checked. Just click the box to uncheck it, and then click the Submit button. Your page is now unpublished and hidden from the public.
To find your unpublished page again, go to the Content list (please read this article for more info on working with the Content list). Right at the top of the page you'll see a group of filters. For 'status' choose 'unpublished' in the drop down box, then click 'Filter'. This will show all of the unpublished content on your site.
Once you find your page you can either go to that page and edit it (changing the publishing options again) or you can check the box to the left of the page title and select 'Publish' in the Update options drop down box at the top of the list.