A D-pad is the cross-shaped directional control found on nearly all modern video game console gamepads and game controllers. Like early video game joysticks, D-pads are digital: they allow input of exactly 8 directions (the points of the compass), with no intermediate values. Although they provide less nuance than analog controls, they can easily be manipulated with very high accuracy using only a single thumb.
D-pads were invented in the 1980s (after traditional joysticks) by Gunpei Yokoi, and his particular design is patented. Initially intended to be a compact controller for the Game & Watch handheld games, it was realized that they would also be appropriate for regular consoles, and Nintendo made the D-pad the standard directional control for the hugely successful Famicom (NES in the rest of the world). Subsequent to this all major video game consoles have had a D-pad. Arcade games, however, have largely continued using joysticks.
A recent trend in modern consoles, beginning with the Nintendo 64, has been to provide both a D-pad and a compact analog stick; depending on the game, one type of control may be more appropriate than the other.