This video is not based on a specific letter, but on multiple fan letters. Eminem even said in an interview that he gets letters as much or more crazy than those of "Stan".
The word "Stan" has become so popular in modern culture that it even entered the Oxford Dictionary in 2018, as a noun (stan) as well as a verb (stans, stanning, stanned). It is described as "An overzealous or obsessive fan of a particular celebrity".
The chorus in this song is sampled from the Dido song "Thank You".
At the end of the video when Eminem realizes that Stan is dead, the window next to him shows lightning flash and you can see Stan staring at him for a brief moment.
"Stan" was the third single from Eminem's third studio album, "The Marshall Mathers LP".