A dice roll (U.K.) or die roll (U.S.) is a roll of one or more dice to provide the random element of a game. This is used extensively in pencil-and-paper games, while in Neverwinter Nights, these rolls are simulated with the pseudo-random generation of a number.
In Neverwinter Nights, determining the success or failure of something typically requires the roll of a 20-sided die (d20), adding modifiers, and comparing the result to a set goal (typically DC or AC). If the modified roll is at least the goal, then the check succeeds. However, when making attack rolls or saving throws, if the die lands on a 1 (natural one), failure is automatic (auto-miss or auto-failure), and if it lands on a 20 (natural twenty), success is automatic (auto-hit or auto-success). These are the only times when auto-failure and auto-success apply; for all other die rolls, a natural twenty is not automatically successful, and a natural one is not automatically failing. Furthermore, there is a server setting that disables auto-failure for saving throws. Among the notable cases where auto-success and auto-failure do not apply (even though many players think otherwise) are skill checks and critical threat rolls.
Example: If a saving throw is being rolled at +7 against a DC of 5, rolling a natural one results in a failed save (unless saving throw auto-failure is disabled) even though 1 + 7 is more than the DC.
The roll of a single die is often described simply as the abbreviation for the die (e.g. d12 for a 12-sided die). So "d6" means a single 6-sided die is rolled; the outcome will be a random number between 1 and 6. The roll of multiple dice that are added together is often described by placing the number of dice before the abbreviation of the die. So "2d4" means two 4-sided dice are rolled, with the results added; the outcome will be a random number between 2 and 8, with 5 being the most likely result. Adding an 'x' to the notation results in a rather different case where a single die is rolled and the result multiplied. That is, "2xd4" means a single 4-sided die is rolled, with the result multiplied by 2; the outcome will be 2, 4, 6, or 8, with each result equally likely. To avoid potential confusion, this latter case is sometimes written in the reversed order, as in "d4 x 2".