A Post Thumbnail is an image that is chosen as the representative image for a Post or Page. The display of this images is up to the theme. This is especially useful for "magazine-style" themes where each post has an image.
Enabling Support for Post Thumbnails
Themes have to declare their support for post images before the interface for assigning these images will appear on the Edit Post and Edit Page screens. They do this by putting the following in their
add_theme_support( 'post-thumbnails' );
To-do: incorporate that information into the Codex