Fate/stay night was a visual novel released in 2004 by Kiniro Nasu, and had three routes, Fate, Unlimited Blade Works, and Heavens Feel. These are theories that fans have created based on these three alternate settings of the same story. Major spoilers ahead.
Due to the three routes in the Fate/stay night Visual Novel, many fans have theorized that each one exists in a paralell univese from each other.
Archer, Shirou Emiya, & Heaven's FeelEdit
During the Heaven's Feel Route of the original Fate/stay night Visual Novel, many have came up with a theory about Archer during that route. It's well known that Archer's true idenitity is Shirou Emiya. During his life, a paralell universe from, the Unlimited Blade Works route presumably, Shirou was a very similar person who how his father, Kiritsugu Emiya, was in Fate/Zero, somewhat of an anti-hero. When you play the Heaven's Feel route and get the Superhero ending, Shirou becomes just like this, going as far as to sacrifice Sakura Matou, his love interest in that route, for the greater good. So, the fans have theorized that after this, The World summoned him as a Counter Guardian Archer Class Servant during the Unlimited Blade Works route.