The d20 System is a tabletop RPG system that uses, among other things, twenty-sided dice.
Most of the d20 System was released as the System Reference Document (SRD) under the Open Game License (OGL) as Open Game Content (OGC), which allows people to make and release supplements for free. This led to multiple game-breaking splatbooks for D&D, and a glut of samey RPGs, mostly because people figured it was worthless to challenge Wizards, and so d20 was soon seen on everygoddamnthing.
Mechanically, d20 is basically a watered down reversed version of the AD&D 2E rules, with huge chunks stolen from Megaversal and SPECIAL, like feats. It works just about as well.
Wizards doesn't use the d20 System any more, as they decided to
fail fuck everyone over change the mechanics for D&D 4th Edition. However, there's still hope for people who RAGE at 4e, since Paizo Games pretty much stole 3.5 and renamed it Pathfinder.
After their temporary bout of insanity, WotC came to their senses and released 5E, releasing Roleplaying games to the mainstream - and going back to what is clearly a lot of 3.X-sensibilities, with a splash of 4E, and even AD&D thrown in for good measure.