Short answers, pulled from the story.
The d20 System is a role-playing game system published in 2000 by Wizards of the Coast. It was originally developed for the 3rd edition of Dungeons and Dragons and is named after the 20-sided die central to its core mechanics.
Jonathan Tweet, Monte Cook, and Skip Williams were the three primary designers. Richard Baker and then-Wizards of the Coast president Peter Adkison also contributed. Many credit Tweet with the basic resolution mechanic, which bears similarities to his earlier game Ars Magica, though Tweet noted the other designers were already using a similar approach when he joined the team.
The Open Game License (OGL), released by Wizards of the Coast in 2000, made the core mechanics of 3rd-edition Dungeons and Dragons permanently open for use, adaptation, and sale by any publisher. The d20 System Trademark License was a separate instrument allowing use of the official d20 logo, but unlike the OGL it could be cancelled by Wizards at any time.
The d20 boom resulted from Wizards of the Coast releasing the Open Game License and d20 Trademark License in 2000, allowing publishers to build on Dungeons and Dragons rules without paying royalties. Companies including Green Ronin, Mongoose Publishing, Goodman Games, and many others entered the market, and the demand helped create an industry for PDF publishing of role-playing games.
Two events in 2003 damaged the d20 publishing market. Wizards of the Coast released edition 3.5 of Dungeons and Dragons at Gen Con 36 in August 2003 with little warning, leaving third-party publishers with outdated books. Separately, Wizards added a "community standards of decency" provision to the trademark license in response to the Book of Erotic Fantasy, demonstrating that Wizards retained broad discretionary power over d20 trademark use.
With the release of 4th-edition Dungeons and Dragons in 2008, Wizards of the Coast revoked the original d20 System Trademark License and replaced it with the Game System License. The new license had no associated OGL or open content. The change did not affect the legal standing of the original OGL, and products based on the earlier SRD could still be published under the OGL.