Pathfinder is an RPG originally derived from the open licensed rules to Dungeons & Dragons v3.5. It was published by Paizo Publishing in 2009.
Pathfinder is a rebranded derivative of the d20 SRD (v3.5), which are the open licensed rules to Dungeons & Dragons v3.5. It is also licensed using the Open Gaming License and its rules are freely available online in the Pathfinder System Reference Document.
Pathfinder was created by Paizo Publishing, the company that was producing Dungeon Magazine and Dragon Magazine for Wizards of the Coast during the 3e/3.5e years. When Dungeons & Dragons Fourth Edition was released and was a significant change in rules and direction from 3.X, and was no longer offered under an open license, Paizo decided to effectively "fork" D&D and continue the original direction of the rules - as a result, some people refer to Pathfinder as "D&D v3.75," as it is mostly compatible with the 3.X branch of D&D.
Playtest materials for Pathfinder Second Edition were released on August 2, 2018; the full product is planned to release in August 2019.
See also: pathfinder-2e