Harvey is a Jimmy Stewart movie about Elwood P. Dowd, a man who is friends with a six foot three white rabbit named Harvey that only he can see. It's...very strange. Most of the plot comes from the fact that Elwood's sister and neice are terribly embarresed by Harvey, and want to have Elwood committed, but they run into trouble when there's a misunderstanding about who the crazy one is. Elwood's sister (Josephine Hull - who also played one of the aunts in Arsenic and Old Lace, fun fact) also sometimes sees Harvey, and throughout the movie, other people have encounters with the rabbit. One of the employees of the insane asylum, when looking up the definition of "Pooka" (It's some sort of spirit guide - that's what Harvey is) finds a message to him written in the encyclopedia - "How are you, Mr. Wilson?"
Harvey talks a lot about mental health - whether Elwood's really crazy, whether everyone else is crazy, whether Harvey exists, whether it's right to commit Elwood, whether it's ethical to change his personality to get rid of a single harmless abnormality. It's not what I expect from a movie from that time period. Elwood does seem genuinely sort of off, too. He goes through the same rituals with everyone he meets, he invites perfect strangers to dinner, he wont let people politely put off these invitations, he drinks a lot, he hangs out in the same place all the time. He's just not quite right. Between that and the way the existence of Harvey is treated (and filmed - Harvey is always in the frame, even though there's nothing there), this comes across to me as a very unique movie, especially for the 50's. I'm surprised that it got made then to be honest, and I'm not surprised that it's remembered.
There's also that really creepy portrait of Jimmy Stewart with the rabbit sitting behind him - I think that contributes to this movie's reputation a lot, because something about it gives the rest of the film just a slightly sinister ambiance. I think most would agree with me when I say that Harvey is a terrifying power (Who can stop time) who just happened to align himself with an unassuming man.