Dungeons & Dragons
Dungeons and Dragons is a role-playing game. Each player becomes a character within the game, and tells the referee, or Dungeon Master, what they will do. Each character belongs to a class, of which there are a number to choose from (core classes such as wizards, fighters, thieves, and priests / clerics and then into less familiar classes, or even "prestige classes" in Third Edition). The game is played with dice containing many different numbers and are referred to by "d + number of sides", i.e. d6 is a six sided die, d20 is a twenty sided die.
D&D falls into the "d20" game system, and just so happens to use that die quite frequently.
D&D is now in it's "4th Edition", released in 2008 and representing major changes in the underlying game system.