Pathfinder is D&D 3.75. Basically, when Wizards of the Coast made D&D 4e and it was a giant change in multiple ways from the most popular 3.5, Paizo decided to release their own system that was an update on the 3.5 rules. The concept of Pathfinder being 'free' is really down to the existence of the OGC, which is basically an srd but more complete.