What, exactly, is "Fate/stay night" supposed to mean? We've all heard of Fate/stay night, the much-beloved visual novel by Type-Moon that taught us that people die when they're killed. 

But what does the title "Fate/stay night" actually mean? We can assume for the moment that "Fate" is just a designator for the series (hence Fate/Zero, Fate/Extra, etc.), but I'm still somewhat baffled as to what "stay night" could possibly be. 

(Nobody on the internet seems to know, and I figure the ultimate answer is probably "it sounds cool", but I thought I'd put this out there anyway.)
When Kinoko Nasu first wrote Fate/Stay Night in college it was called Old Fate (旧Fate) and Fate Origin and was reimagined later to be Fate/Prototype. Nasu only wrote what would become the game's Fate Route.

there is speculation on what meaning there is behind the name. ie


Fate may refer to the fate of the servants like Saber accepting her fate in her life or the Fate of magi that battle each other in the war
Stay may refer to the desire to keep the servants like with Shirou and Saber, it may refer to make something remain or stay like the reason why Shiro enters the war in both Fate/Stay Night and Fate/Hollow Ataraxia was to keep the peace in the town or in Heaven's Feel Route which is like the ultimate climax to the game how Zouken wanted Heaven's Feel to become Immorality but without his body rotting. in Fate/Extra, Twice H. Pieceman had changed the Moon Cell's selection process to be a war believing humanity requires war to advance and evolve, he wanted Hakuno Kishinami and every other Master who appeared at the Moon Cell's core to wish for the perpetuation of war (stay in war)
Night could refer to how the battles mainly occurred during the night during the night or the darkness behind the war (In Prototype the Heaven's Feel system was meant to materialize Beast or in Fate/Stay Night Angra Mainyu's corruption of the grail)


Another theory is that the Fate part was taken from his original work, /Stay Night was just added to sound cool like with Kara no Kyoukai (空の境界?, lit. Boundary of Emptiness) - The Garden of Sinners or Tsukihime (月姫, lit. Moon Princess).

ref Anime News Network Forums