A directory is another name for a folder. Files on your hard disk are organized into various folders, or directories, so that it is easier to keep track of them. For example, you may keep your pictures in one folder and your music files in another folder. Folders can also contain other folders, allowing for more specific organization.
Since you can have folders within a folder, files on your hard drive are organized much like branches on a tree. The main directory on your hard drive is appropriately called the "root directory." Folders that exist within the root directory most likely contain other folders, which may branch out to even more folders.
When you are browsing one directory and want to open the folder that contains the current directory, it is called "moving up a directory." As you move up directories, you will eventually move up to the root directory. In Windows, this may be your C:\ directory, while on the Mac it will be the name of your hard drive, such as "Macintosh HD."