The folder pane is displayed on the left side of the Thunderbird window. It shows a list of your email accounts, the folders that are created by default (such as "Sent", "Trash", etc) and the folders that you have manually created to organize your messages.
There are several "views" that can be used to display in the folder pane. The view you select will determine how the folders are organized and displayed (while not affecting the actual folders or messages themselves.) Select View > Folders from the menu bar, or select Folders from the application menu, to choose the view you want to use. The following options are available:
In Thunderbird versions before 8.0, the folder pane had a title bar showing the name of the current view. To the right of the name there were arrow buttons that could be used for rotating back and forth through the available views. However, the title bar and arrow buttons were removed in Thunderbird 8.0. If you would like to reinstate these buttons, install the Folder Pane View Switcher add-on. (Note that third-party add-ons are not supported by Mozilla.)
This add-on also has another useful folder feature. If your displayed view is something other than "All Folders" and you are in the middle of a drag-and-drop operation and you realize that you want to drop into a folder that isn't listed in your current view, hovering your mouse briefly over the folder pane title bar will cause it to automatically switch to the "All Folders" view. It will switch back to your prior view when you're done with the drag-and-drop.