The specific hardware implementation of a direction pad can vary. One common approach is to make the direction pad a plus-shaped piece floating on a set of digital pushbuttons. Pressing one of the four cardinal directions on the plus depresses the button underneath (up, down, left, right), pressing a diagonal direction depresses two buttons (down and right, or up and left for example).
Whatever the specific hardware implementation, the input is used in a similar manner to that of a four way joystick, to move a character, cursor, highlight an option in a menu, or the like.
The Sega Genesis controller possesses the D-Pad and utilizes the cardinal directions as well as the diagonal directional capabilities in a variety of its games, including Toejam and Earl
The Sony PSP has a kind of multi-directional pad that acts as a combination of a control stick and a Directional pad in which you push it in the direction you wish to go, but not in just the standard 8 directions.