A 20-sided polyhedral die. Shaped like an Icosahedron.
In Dungeons & Dragons and many other tabletop games, the d20 is the most important die and the one rolled most often. Almost any action a character takes which can either succeed or fail, in particular nearly any attempt to damage a target with a weapon is modeled with a d20 roll.
Rolling a value of 1 or 20 on a d20 "naturally" (i.e. before adding or subtracting modifiers) is considered special: a 20 being a "critical success" and a 1 being a "Critical Failure". What this specifically entails varies, but often it guarantees success or failure and/or results in an extra-good outcome (such as a Critical Hit) or extra-bad outcome (such as some mishap occurring).