Every page in a concrete5 site is part of one unified hierarchy called your site tree. Every site must have just one root or home level, and every page sits somewhere below - under its parent. You can see this whole sitemap by going to Dashboard > Sitemap.
When you use the Add Page button from your in-context editing toolbar, you are adding a child to the page you are on. The folder and page icons used in the sitemap are there to show you at a glance if a page has children, there is no typed difference between a page that has children and one that does not.
When we first started thinking about Concrete CMS we thought in terms of loose collections of data, and the whole "network" model of organizing data that feels more accurate to what happens on the web. While it is true from a literal sense that many websites don't strictly follow a hierarchy in every detail, the majority do in some respects. The advantages you get in organizing your pages this way are many. Permissions for who can do what to which pages tend to trickle down a tree easily. Themes and page types are automatically set based on their parent. Navigations can easily build themselves by being configured to look at and display parts of the site tree. People have a good sense of how their computers are organized into Folders and Files and we've found that this single hierarchy creates a reassuring spine to even complicated sites that may break outside of the tree in ways.
Pages can be aliased to show up at more than one spot on the tree. When this is the case, the page still has a single parent, but alias relationships may point to that page from other spots on the tree. Following an alias link takes you to the page in question, which behaves as it would if you arrived at it from its true parent.
Various pages exist in concrete5 for utility purposes. This includes login, register, various error pages, and everything you see in your site Dashboard. 
All of these are pages you can manage through concrete5's permission structure as well. In your Dashboard > Sitemap there is a checkbox for showing these pages. Turning this checkbox on also displays all the Single Pages your site contains.
The sitemap has three view modes: Tree, Folder, and Search. For smaller sites the tree view will be all you use. If you have a large site and need to search for specific pages, the search interface is very helpful. Search also lets you select multiple pages and perform bulk changes which can be quite helpful. Folder view was introduced to deal with sites that may contain many pages at a single level. If you're dealing with thousands of pages in one node, the Javascript of the Sitemap can become unwieldy and switching to Folder view is helpful. You can choose which mode your concrete5 install defaults to form Dashboard > Sitewide Settings
You can change anything about a page from the Dashboard > Sitemap. Clicking any page name in the list brings up a menu that maps to the same settings you see in the In-context toolbar in edit mode. The only thing here that can't easily be un-done is Delete. When you delete a page, it's gone. Period. That's why we ask to make sure.
You can also move or copy a page by simply dragging it by the icon to a new parent. Once you've picked a new parent you will be asked if you want to Move, Alias, Copy, or Copy with Children.
If you'd like to change the sort order of pages at a given level, just drag and drop the page icon to its new location in the list. Look for a thin black line showing that you're dropping the page in the right place.
Many navigation blocks take advantage of the sort order defined here.
We use the Sitemap throughout the concrete5 editing experience. If you Move/Copy a page from the In-context editing toolbar you will see this same interface in an overlay window asking you for a new target.
If you use the Page List block to display a list of pages from a specific spot on the tree, you can use the Sitemap to choose the spot. If you are a developer looking to incorporate the Sitemap into your add-on, check out the Page Selector in the Developers Guide.