Fate/stay night was a visual novel released in 2004 by Kiniro Nasu, and had three routes, Fate, Unlimited Blade Works, and Heavens Feel. The following are theories that fans have created based on those three alternate settings of the same story.  Major spoilers ahead.  

Parallel Universe

Due to the three routes in the Fate/stay night Visual Novel, many fans have theorized that each one exists in a parallel universe from each other.  

Archer, Shirou Emiya, & Heaven's Feel

Many theories have been posited about Archer during the Heaven's Feel Route of the original Fate/stay night Visual Novel. It's well known that Archer's true identify is Shirou Emiya.  During his life, presumably a parallel universe from the Unlimited Blade Works route, Shirou was very similar to how his father, Kiritsugu Emiya, was in Fate/Zero, in that he was something of an anti-hero. When you play the Heaven's Feel route and get the Superhero ending, Shirou becomes just like this, going so far as to sacrifice Sakura Matou, his love interest in that route, for the greater good. Consequently, the fans have theorized that after this The World summoned him as a Counter Guardian Archer Class Servant during the Unlimited Blade Works route.