The song is the story of an obsessed fan named Stanley ‘Stan’ Mitchell who writes letters to the rapper and gets angry when there is no reply. The story ends tragically when Stan kills his pregnant girlfriend.
‘Stan’ is an informal word as entered in the Oxford Dictionary.
Noun: ‘An overzealous or obsessive fan of a particular celebrity.’
Verb: ‘Be an overzealous or obsessive fan of a particular celebrity.’
The dictionary credits Eminem with the origin of the word.