Dice are polyhedral objects used to generate random numbers, and are the focus of all RPGs except the weird creepy ones where they use, like, cards or something.
Dice are typically given the name formula d#, where # is the number of sides. Ergo twenty-sided dice are called d20s, eight-sided dice are called d8s, and so on. The one exception to this seems to be the d100, which is typically two ten-sided dice - one for the tens, one for the units.
The d20 is often seen as the universal symbol for gaming, because nobody else will touch it. It's become a bit cliché due to overuse.